0011 chapter iv
•Download as DOCX, PDF•
1 like•952 views
This document provides instruction on solving various types of equations, including quadratic equations, equations containing radicals, and equations that can be reduced to quadratic form. It includes examples of solving equations that are quadratic in form by rewriting them in standard form and substituting a variable, then solving the resulting quadratic equation. It also provides examples of solving equations containing radicals by isolating radicals and raising both sides of the equation to appropriate powers. Students are expected to learn to identify different equation types, select appropriate solution methods, and solve various quadratic and radical equations.
Report
Share
Report
Share
![Chapter IV<br />Much of the study in quadratic equation consist of different solving equation, we have equation in quadratic form, equation containing radicals and equation reducible to quadratic equation. They have their own steps and procedures to be followed in order to solve the given equation. <br /> TARGET SKILLS: <br />At the end of this chapter, students are expected to:<br />• discuss solving equation on quadratic;<br />• determine the index and its radicals;<br /> • interpret the solution of the original equation; and<br />• select appropriate method in solving quadratic equation.<br />Lesson 10<br />Equation in Quadratic Form<br />OBJECTIVES:<br />At the end of this lesson, students are expected to:<br />identify equation in quadratic form;<br />select appropriate method in solving quadratic equation; and<br />change the equation in standard form.<br />Quadratic in Form<br />An equation is quadratic in form when it can be written in this standard form<br />where the same expression is inside both ( )'s.<br /> In other words, if you have a times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.<br /> Solving Equations that are Quadratic in Form<br />Step 1: Write in Standard Form, , if needed. <br />If it is not in standard form, move any term(s) to the appropriate side by using the addition/subtraction property of equality. Also, make sure that the squared term is written first left to right, the expression not squared is second and the constant is third and it is set equal to 0.<br />Step 2: Substitute a variable in for the expression that follows b in the second term. <br />In other words, substitute your variable for what is in the ( ) when it is in standard form, . I’m going to use t for my substitution, but really you can use any variable as long as it is not the variable that is used in the original equation.<br />Step 3: Solve the quadratic equation created in step 2. <br />You can use any method you want to solve the quadratic equation: factoring, completing the square or quadratic formula.<br />Step 4: Find the value of the variable from the original equation. <br />Keep in mind that you are finding a solution to the original equation and that the variable you substituted in for in step 2 is not your original variable. Use the substitution that was used to set up step 2 and then solve for the original variable.<br />Step 5: Check your solutions. <br />In some cases, you will be working with rational exponents and square roots in your problems. Those types of equations can cause extraneous solutions. Recall that an extraneous solution is one that is a solution to an equation after doing something like raising both sides of an equation by an even power, but is not a solution to the original problem. Even though not all of the quadratic in form equations can cause extraneous solutions, it is better to be safe than sorry and just check them all.<br />Example 1: Solve the equation that is quadratic in form: .<br />Standard Form, <br />*Rewriting original equation to show it is quadratic in form *Note that (y squared) squared = y to the fourth *When in stand. form, let t = the expression following b.<br /> <br />Next, we need to substitute t in for y squared in the original equation. <br /> <br />*Original equation *Substitute t in for y squared<br />Note how we ended up with a quadratic equation when we did our substitution. From here, we need to solve the quadratic equation that we have created.<br /> <br />Solve the quadratic equation: factoring, completing the square or quadratic formula. <br />*Factor the trinomial *Use Zero-Product Principle *Set 1st factor = 0 and solve *Set 2nd factor = 0 and solve <br />Let's find the value(s) of y when t = -4:<br />*Plug in - 4 for t *Use square root method to solve for y *First solution *Second solution <br />Let's find the value(s) of y when t = 1:<br />*Plug in 1 for t *Use square root method to solve for y *First solution *Second solution <br />Example 2: Solve the equation that is quadratic in form: .<br /> Standard Form, <br /> <br />*Inverse of add. 3 is sub. 3 *Equation in standard form<br />Note how when you square x to the 1/3 power you get x to the 2/3 power, which is what you have in the first term.<br />* Rewriting original equation to show it is quadratic in form *Note that (x to the 1/3 power) squared = x to the 2/3 power *When in stand. form, let t = the expression following b.<br />Next, we need to substitute t in for x to the 1/3 power in the original equation. <br />*Original equation *Substitute t in for x to the 1/3 power<br /> <br />You can use any method you want to solve the quadratic equation: factoring, completing the square or quadratic formula.<br />*Factor the trinomial *Use Zero-Product Principle *Set 1st factor = 0 and solve *Set 2nd factor = 0 and solve <br /> <br />Let's find the value(s) of x when t = 3:<br />*Plug in 3 for t *Solve the rational exponent equation *Inverse of taking it to the 1/3 power is raising it to the 3rd power<br /> <br />Let's find the value(s) of x when t = -1:<br /> <br />*Plug in -1 for t *Solve the rational exponent equation *Inverse of taking it to the 1/3 power is raising it to the 3rd power<br />Let's double check to see if x = 27 is a solution to the original equation.<br />*Plugging in 27 for x *True statement<br /> <br />Since we got a true statement, x = 27 is a solution.<br />Let's double check to see if x = -1 is a solution to the original equation.<br /> <br />*Plugging in -1 for x *True statement<br />Since we got a true statement, x = -1 is a solution.<br />There are two solutions to this equation: x = 27 and x = -1.<br />Exercises:<br />,[object Object]](https://image.slidesharecdn.com/0011chapteriv-100531014415-phpapp02/85/0011-chapter-iv-1-320.jpg)
Recommended
Nature of the roots and sum and product of the roots of a quadratic equation
Provides example and solutions about about how to find the roots of a quadratic equation and its sum and product.
Sum and product of the roots of a
The document discusses how to find the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0. It provides the formulas that the sum of the roots is equal to -b/a and the product of the roots is equal to c/a. It then works through two examples of using these formulas to find the sum and product of the roots of equations 3x^2 + 4x - 5 = 0 and 4x^2 - 29x - 24 = 0. The solutions show the steps of identifying a, b, c and then applying the formulas to determine the sum and product of the roots for each example equation.
Quadratic equations lesson 3
The document discusses various methods for solving quadratic equations, including factoring, square root method, completing the square, and the quadratic formula. It also covers solving other types of equations that are quadratic in form, such as radical equations, through transformations. The objectives are to solve quadratic, radical, and other equations that are quadratic in form and to find sums and products of roots, the quadratic equation given roots, and solve application problems involving these equation types.
Quadratic Equations
FREE MCA NATIONAL LEVEL MOCK TEST
Click on link given below:
www.tcyonline.com/activatefree.php?id=14
TCYonline.com
No.1 Testing Platform
nature of the roots and discriminant
This document provides guidance on identifying the nature of roots of quadratic equations. It begins by identifying the least mastered skill of identifying the nature of roots. It then reviews the standard form of a quadratic equation and the quadratic formula. The key concept of the discriminant is explained, which determines the number and type of roots. Examples are provided to show how to find the discriminant and use it to describe the nature of roots. Activities are included for students to practice rewriting equations in standard form, finding a, b, c values, calculating discriminants, and determining the nature of roots. An assessment card with example problems is provided to check understanding.
Strategic intervention material discriminant and nature of the roots
This document provides guidance on identifying the nature of roots for quadratic equations. It begins by explaining that the discriminant, which is calculated as b^2 - 4ac, can be used to determine if the roots are real, rational, equal, etc. Several examples are worked through to demonstrate rewriting equations in standard form, finding a, b, and c values, and calculating the discriminant. Activities are included for students to practice these skills. The document concludes by summarizing that a positive discriminant indicates real, unequal roots, a negative discriminant indicates non-real roots, and a zero discriminant indicates real, equal roots.
Assure
This document provides an outline for a lesson plan on quadratic equations. The objectives are to define quadratic equations, state their form, solve problems involving them, identify their use in everyday life, and evaluate performance. An introduction defines quadratic equations as ax2+bx+c=0 and explains their solving methods. A warm-up activity involves grouping students and having them determine if equations are quadratic. The main activity groups students to solve quadratic equations using different methods. A conclusion discusses the various uses of quadratic equations and summarizes the solving methods. A feedback survey ends the document.
Quadratic equations
This document defines and explains how to solve quadratic equations. A quadratic equation is an equation that can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. There are several methods for solving quadratic equations covered in the document: factoring, taking the square root, completing the square, and using the quadratic formula. The discriminant, b^2 - 4ac, determines the number and type of solutions.
Recommended
Nature of the roots and sum and product of the roots of a quadratic equation
Provides example and solutions about about how to find the roots of a quadratic equation and its sum and product.
Sum and product of the roots of a
The document discusses how to find the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0. It provides the formulas that the sum of the roots is equal to -b/a and the product of the roots is equal to c/a. It then works through two examples of using these formulas to find the sum and product of the roots of equations 3x^2 + 4x - 5 = 0 and 4x^2 - 29x - 24 = 0. The solutions show the steps of identifying a, b, c and then applying the formulas to determine the sum and product of the roots for each example equation.
Quadratic equations lesson 3
The document discusses various methods for solving quadratic equations, including factoring, square root method, completing the square, and the quadratic formula. It also covers solving other types of equations that are quadratic in form, such as radical equations, through transformations. The objectives are to solve quadratic, radical, and other equations that are quadratic in form and to find sums and products of roots, the quadratic equation given roots, and solve application problems involving these equation types.
Quadratic Equations
FREE MCA NATIONAL LEVEL MOCK TEST
Click on link given below:
www.tcyonline.com/activatefree.php?id=14
TCYonline.com
No.1 Testing Platform
nature of the roots and discriminant
This document provides guidance on identifying the nature of roots of quadratic equations. It begins by identifying the least mastered skill of identifying the nature of roots. It then reviews the standard form of a quadratic equation and the quadratic formula. The key concept of the discriminant is explained, which determines the number and type of roots. Examples are provided to show how to find the discriminant and use it to describe the nature of roots. Activities are included for students to practice rewriting equations in standard form, finding a, b, c values, calculating discriminants, and determining the nature of roots. An assessment card with example problems is provided to check understanding.
Strategic intervention material discriminant and nature of the roots
This document provides guidance on identifying the nature of roots for quadratic equations. It begins by explaining that the discriminant, which is calculated as b^2 - 4ac, can be used to determine if the roots are real, rational, equal, etc. Several examples are worked through to demonstrate rewriting equations in standard form, finding a, b, and c values, and calculating the discriminant. Activities are included for students to practice these skills. The document concludes by summarizing that a positive discriminant indicates real, unequal roots, a negative discriminant indicates non-real roots, and a zero discriminant indicates real, equal roots.
Assure
This document provides an outline for a lesson plan on quadratic equations. The objectives are to define quadratic equations, state their form, solve problems involving them, identify their use in everyday life, and evaluate performance. An introduction defines quadratic equations as ax2+bx+c=0 and explains their solving methods. A warm-up activity involves grouping students and having them determine if equations are quadratic. The main activity groups students to solve quadratic equations using different methods. A conclusion discusses the various uses of quadratic equations and summarizes the solving methods. A feedback survey ends the document.
Quadratic equations
This document defines and explains how to solve quadratic equations. A quadratic equation is an equation that can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. There are several methods for solving quadratic equations covered in the document: factoring, taking the square root, completing the square, and using the quadratic formula. The discriminant, b^2 - 4ac, determines the number and type of solutions.
2.quadratic equations
This document contains 14 problems involving quadratic equations. The problems cover expressing quadratic equations in standard form, finding roots of quadratic equations, determining the range of values for constants in quadratic equations, and relating the roots and coefficients of quadratic equations. Sample solutions are provided for each problem.
Quadratic equations
The document defines quadratic equations as polynomial equations of the second degree where the highest exponent on the variable is 2. It provides the general form of a quadratic equation as ax2 + bx + c = 0 where a, b, and c are constants and a ≠ 0. Roots or solutions of a quadratic equation are the values that make the equation equal to 0. The document discusses several methods for solving quadratic equations including factoring, using the quadratic formula, and completing the square. It provides examples of solving quadratic equations using each of these methods.
Nature of the roots of a quadratic equation
The discriminant of a quadratic equation is represented by b^2 - 4ac. This value determines the nature of the roots. If b^2 - 4ac = 0, then the roots are real and equal. If b^2 - 4ac > 0, then the roots are real but unequal. If b^2 - 4ac < 0, then the roots are imaginary and unequal. The document provides examples of calculating the discriminant and determining the nature of roots for different quadratic equations.
Mathematics 9 Lesson 1-C: Roots and Coefficients of Quadratic Equations
This powerpoint presentation discusses or talks about the topic or lesson Roots and Coefficients of Quadratic Equations. It also discusses and explains the rules, steps and examples of Roots and Coefficients of Quadratic Equations
Illustrates quadratic equation
This document discusses quadratic equations. It defines a quadratic equation as an equation of degree 2 that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It provides examples of complete and incomplete quadratic equations. It also shows how to identify if an equation is quadratic or not and how to transform equations into standard form (ax2 + bx + c = 0) in order to identify the values of a, b, and c.
Quadratic equations
Quadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 – 4 = 0
Solution:
x2 – 4 = 0
x2 = 4
√x² = √4
x = ± 2
5.Example 2. Solve: 5x² - 11 = 49
Solution:
5x² - 11 = 49
5x² = 49 + 11
5x² = 60
x² = 12
x = ±√12
x = ±2√3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x² = 6x - 8
Solution:
x² = 6x – 8
x² - 6x + 8 = 0
(x – 4)(x – 2) = 0
x – 4 = 0 | x – 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x² is not 1, divide every term by this coefficient so as to make the coefficient of x² equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a ± sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x² - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x² - 2x - 7 = 0
12.Solve the following:
1. x² - 15x – 56 = 0
2. 7x² = 2x + 6
3. 9x² - 3x + 8 = 0
4. 8x² + 9x -144 = 0
5. 2x² - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x² - 5x + 6 = 0 1. x² - 7x + 6 = 0
2. 3 x² = x + 2 2. 10 x² - 13x – 3 = 0
3. 2 x² - 11x + 12 = 0 3. x (5x – 4) = 2
By Completing the Square
1. x² + 6x + 5 = 0
2. x² - 8x + 3 = 0
3. 2 x² + 3x – 5 = 0
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
This powerpoint presentation discusses or talks about the topic or lesson Solving Quadratic Equations using the Quadratic Formula. It also discusses the steps in solving quadratic equations using the method of Quadratic Formula.
Module 10 Topic 4 solving quadratic equations part 1
This document provides instruction on solving quadratic equations. It begins with an introduction explaining why quadratic equations are useful and includes a video example. It then defines quadratic equations and provides examples of solving quadratic equations by factoring and using the quadratic formula. The document uses examples and "Try It" problems for students to practice each step in solving quadratic equations.
Quadratic equations ppt
The document discusses solving quadratic equations using various techniques like factoring, completing the square, and the quadratic formula. It provides examples of using these methods to solve equations in standard form. The quadratic formula is derived and explained. The concept of the discriminant is introduced and how it relates to the number and type of solutions. An example problem is worked through applying the Pythagorean theorem and quadratic formula to solve a real world word problem.
Strategic intervention materials on mathematics 2.0
This document provides teaching materials on solving quadratic equations by factoring for a mathematics class. It includes an overview of quadratic equations and their standard form. It then outlines least mastered skills and activities to practice identifying quadratic equations, rewriting them in standard form, factoring trinomials, and determining roots. Example problems and solutions are provided to demonstrate factoring trinomials and using factoring to solve quadratic equations. A practice problem asks students to solve a word problem involving a quadratic equation. Key terms and concepts are bolded. References for further reading are listed at the end.
QUADRATIC EQUATIONS
This document discusses four methods for solving quadratic equations: factorization, completing the square, using a formula, and using graphs. It provides an example of solving the equation 2x^2 - 10x + 12 + x^2 + 6x = -9 by factorizing into (x - 3)(x - 1) = 0, finding that the solutions are x = 3 or x = 1.
Solving quadratic equations using the quadratic formula
The document provides instructions on solving quadratic equations using the quadratic formula. It begins by presenting the formula: x = -b ± √(b^2 - 4ac) / 2a. It then works through three examples of applying the formula step-by-step: solving 2x^2 - 5x - 3 = 0, solving 2x^2 + 7x = 9, and solving x^2 + x - 1 = 0. Each example shows identifying the a, b, and c coefficients and plugging them into the formula to solve for x.
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Provides examples and solutions on how to solve equations that is transformable to quadratic equation and rational algebraic equations.
Presentation on quadratic equation
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
Quadratic And Roots
This document discusses quadratic equations and their properties. It defines quadratic equations as equations of the form y=ax^2 +bx + c, where the highest power is 2. It explains that quadratic equations can be solved using the quadratic formula, x = -b ± √(b^2 - 4ac) / 2a. The number of solutions depends on the discriminant, b^2 - 4ac. If it is greater than 0, there are two solutions, if equal to 0 there is one solution, and if less than 0 there are no solutions. Examples are provided to demonstrate solving quadratic equations.
Quadratic Equations (Quadratic Formula) Using PowerPoint
This document summarizes the steps to solve a quadratic equation using the quadratic formula. It works through solving the specific equation 5y^2 - 8y + 3 = 0 as an example. The key steps are: 1) Identifying the coefficients a, b, and c; 2) Plugging these into the quadratic formula; 3) Simplifying the terms; 4) Isolating the variable to find the solutions of 1 and 0.6. These solutions are then checked by substituting them back into the original equation.
Quadratic equation basic
An equation of the form ax^2 + bx + c = 0 is the general form of a quadratic equation, where a, b, and c are real numbers, a is not equal to 0, a is the coefficient of x^2, b is the coefficient of x, and c is the constant. Examples given are x^2 - 3x + 2 = 0 and 6x^2 + x + 1 = 0.
Quadratic Formula Presentation
The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.
Quadratic Equations
The document discusses the quadratic formula and how to use the discriminant to determine the number of solutions a quadratic equation has. It provides examples of calculating the discriminant for different quadratic equations and relating the discriminant to whether there are 0, 1, or 2 solutions graphically.
The discriminant
The document discusses the discriminant and how it is used to determine the number of solutions to a quadratic equation. The discriminant, b^2 - 4ac, is calculated and compared to 0 to find the number of solutions: if greater than 0 there are 2 solutions, if equal to 0 there is 1 solution, if less than 0 there are no real solutions. Several examples are shown of calculating the discriminant and determining the nature of the roots. The document also discusses how to find the value of a variable if the roots are equal.
diploma
This document is a certificate confirming that a student successfully completed their matriculation exam. It provides the student's personal details like date of birth and place of residence. It lists the subjects and grades the student received on the matriculation exam, and confirms they passed with an overall grade point average of 4.33. The certificate is issued by the Ministry of Education of Serbia.
More Related Content
What's hot
2.quadratic equations
This document contains 14 problems involving quadratic equations. The problems cover expressing quadratic equations in standard form, finding roots of quadratic equations, determining the range of values for constants in quadratic equations, and relating the roots and coefficients of quadratic equations. Sample solutions are provided for each problem.
Quadratic equations
The document defines quadratic equations as polynomial equations of the second degree where the highest exponent on the variable is 2. It provides the general form of a quadratic equation as ax2 + bx + c = 0 where a, b, and c are constants and a ≠ 0. Roots or solutions of a quadratic equation are the values that make the equation equal to 0. The document discusses several methods for solving quadratic equations including factoring, using the quadratic formula, and completing the square. It provides examples of solving quadratic equations using each of these methods.
Nature of the roots of a quadratic equation
The discriminant of a quadratic equation is represented by b^2 - 4ac. This value determines the nature of the roots. If b^2 - 4ac = 0, then the roots are real and equal. If b^2 - 4ac > 0, then the roots are real but unequal. If b^2 - 4ac < 0, then the roots are imaginary and unequal. The document provides examples of calculating the discriminant and determining the nature of roots for different quadratic equations.
Mathematics 9 Lesson 1-C: Roots and Coefficients of Quadratic Equations
This powerpoint presentation discusses or talks about the topic or lesson Roots and Coefficients of Quadratic Equations. It also discusses and explains the rules, steps and examples of Roots and Coefficients of Quadratic Equations
Illustrates quadratic equation
This document discusses quadratic equations. It defines a quadratic equation as an equation of degree 2 that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It provides examples of complete and incomplete quadratic equations. It also shows how to identify if an equation is quadratic or not and how to transform equations into standard form (ax2 + bx + c = 0) in order to identify the values of a, b, and c.
Quadratic equations
Quadratic Equations
In One Variable
1. Quadratic Equation
an equation of the form
ax2 + bx + c = 0
where a, b, and c are real numbers
2.Types of Quadratic Equations
Complete Quadratic
3x2 + 5x + 6 = 0
Incomplete/Pure Quadratic Equation
3x2 - 6 = 0
3.Solving an Incomplete Quadratic
4.Example 1. Solve: x2 – 4 = 0
Solution:
x2 – 4 = 0
x2 = 4
√x² = √4
x = ± 2
5.Example 2. Solve: 5x² - 11 = 49
Solution:
5x² - 11 = 49
5x² = 49 + 11
5x² = 60
x² = 12
x = ±√12
x = ±2√3
6.Solving Quadratic Equation
7.By Factoring
Place all terms in the left member of the equation, so that the right member is zero.
Factor the left member.
Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
8.Example: x² = 6x - 8
Solution:
x² = 6x – 8
x² - 6x + 8 = 0
(x – 4)(x – 2) = 0
x – 4 = 0 | x – 2 = 0
x = 4 x = 2
9.By Completing the Square
Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x² is not 1, divide every term by this coefficient so as to make the coefficient of x² equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
Find the square root of both members, placing a ± sign before the square root of the right member.
Solve the resulting equation for x.
10.Example: x² - 8x + 7 = 0
11.By Quadratic Formula
Example: 3x² - 2x - 7 = 0
12.Solve the following:
1. x² - 15x – 56 = 0
2. 7x² = 2x + 6
3. 9x² - 3x + 8 = 0
4. 8x² + 9x -144 = 0
5. 2x² - 3 + 12x
13.Activity:
Solve the following quadratic formula.
By Factoring By Quadratic Formula
1. x² - 5x + 6 = 0 1. x² - 7x + 6 = 0
2. 3 x² = x + 2 2. 10 x² - 13x – 3 = 0
3. 2 x² - 11x + 12 = 0 3. x (5x – 4) = 2
By Completing the Square
1. x² + 6x + 5 = 0
2. x² - 8x + 3 = 0
3. 2 x² + 3x – 5 = 0
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
This powerpoint presentation discusses or talks about the topic or lesson Solving Quadratic Equations using the Quadratic Formula. It also discusses the steps in solving quadratic equations using the method of Quadratic Formula.
Module 10 Topic 4 solving quadratic equations part 1
This document provides instruction on solving quadratic equations. It begins with an introduction explaining why quadratic equations are useful and includes a video example. It then defines quadratic equations and provides examples of solving quadratic equations by factoring and using the quadratic formula. The document uses examples and "Try It" problems for students to practice each step in solving quadratic equations.
Quadratic equations ppt
The document discusses solving quadratic equations using various techniques like factoring, completing the square, and the quadratic formula. It provides examples of using these methods to solve equations in standard form. The quadratic formula is derived and explained. The concept of the discriminant is introduced and how it relates to the number and type of solutions. An example problem is worked through applying the Pythagorean theorem and quadratic formula to solve a real world word problem.
Strategic intervention materials on mathematics 2.0
This document provides teaching materials on solving quadratic equations by factoring for a mathematics class. It includes an overview of quadratic equations and their standard form. It then outlines least mastered skills and activities to practice identifying quadratic equations, rewriting them in standard form, factoring trinomials, and determining roots. Example problems and solutions are provided to demonstrate factoring trinomials and using factoring to solve quadratic equations. A practice problem asks students to solve a word problem involving a quadratic equation. Key terms and concepts are bolded. References for further reading are listed at the end.
QUADRATIC EQUATIONS
This document discusses four methods for solving quadratic equations: factorization, completing the square, using a formula, and using graphs. It provides an example of solving the equation 2x^2 - 10x + 12 + x^2 + 6x = -9 by factorizing into (x - 3)(x - 1) = 0, finding that the solutions are x = 3 or x = 1.
Solving quadratic equations using the quadratic formula
The document provides instructions on solving quadratic equations using the quadratic formula. It begins by presenting the formula: x = -b ± √(b^2 - 4ac) / 2a. It then works through three examples of applying the formula step-by-step: solving 2x^2 - 5x - 3 = 0, solving 2x^2 + 7x = 9, and solving x^2 + x - 1 = 0. Each example shows identifying the a, b, and c coefficients and plugging them into the formula to solve for x.
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Provides examples and solutions on how to solve equations that is transformable to quadratic equation and rational algebraic equations.
Presentation on quadratic equation
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
Quadratic And Roots
This document discusses quadratic equations and their properties. It defines quadratic equations as equations of the form y=ax^2 +bx + c, where the highest power is 2. It explains that quadratic equations can be solved using the quadratic formula, x = -b ± √(b^2 - 4ac) / 2a. The number of solutions depends on the discriminant, b^2 - 4ac. If it is greater than 0, there are two solutions, if equal to 0 there is one solution, and if less than 0 there are no solutions. Examples are provided to demonstrate solving quadratic equations.
Quadratic Equations (Quadratic Formula) Using PowerPoint
This document summarizes the steps to solve a quadratic equation using the quadratic formula. It works through solving the specific equation 5y^2 - 8y + 3 = 0 as an example. The key steps are: 1) Identifying the coefficients a, b, and c; 2) Plugging these into the quadratic formula; 3) Simplifying the terms; 4) Isolating the variable to find the solutions of 1 and 0.6. These solutions are then checked by substituting them back into the original equation.
Quadratic equation basic
An equation of the form ax^2 + bx + c = 0 is the general form of a quadratic equation, where a, b, and c are real numbers, a is not equal to 0, a is the coefficient of x^2, b is the coefficient of x, and c is the constant. Examples given are x^2 - 3x + 2 = 0 and 6x^2 + x + 1 = 0.
Quadratic Formula Presentation
The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.
Quadratic Equations
The document discusses the quadratic formula and how to use the discriminant to determine the number of solutions a quadratic equation has. It provides examples of calculating the discriminant for different quadratic equations and relating the discriminant to whether there are 0, 1, or 2 solutions graphically.
The discriminant
The document discusses the discriminant and how it is used to determine the number of solutions to a quadratic equation. The discriminant, b^2 - 4ac, is calculated and compared to 0 to find the number of solutions: if greater than 0 there are 2 solutions, if equal to 0 there is 1 solution, if less than 0 there are no real solutions. Several examples are shown of calculating the discriminant and determining the nature of the roots. The document also discusses how to find the value of a variable if the roots are equal.
What's hot (20)
Mathematics 9 Lesson 1-C: Roots and Coefficients of Quadratic Equations
Mathematics 9 Lesson 1-C: Roots and Coefficients of Quadratic Equations
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Module 10 Topic 4 solving quadratic equations part 1
Module 10 Topic 4 solving quadratic equations part 1
Strategic intervention materials on mathematics 2.0
Strategic intervention materials on mathematics 2.0
Solving quadratic equations using the quadratic formula
Solving quadratic equations using the quadratic formula
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Solving Equations Transformable to Quadratic Equation Including Rational Alge...
Quadratic Equations (Quadratic Formula) Using PowerPoint
Quadratic Equations (Quadratic Formula) Using PowerPoint
Viewers also liked
diploma
This document is a certificate confirming that a student successfully completed their matriculation exam. It provides the student's personal details like date of birth and place of residence. It lists the subjects and grades the student received on the matriculation exam, and confirms they passed with an overall grade point average of 4.33. The certificate is issued by the Ministry of Education of Serbia.
Implantação da avaliação especial de desempenho no município de vitória
I. O documento descreve a implantação do sistema de avaliação especial de desempenho para servidores em estágio probatório no município de Vitória; II. O sistema avalia os servidores em dois períodos durante o estágio probatório de três anos para determinar sua aptidão para o cargo; III. Os servidores aprovados na avaliação tornam-se estáveis e os reprovados são exonerados.
Circulo cromatico e gamas
El documento trata sobre la asignatura de Educación Plástica y Visual en el I.E.S. No 1 de A Estrada, impartida por el profesor A. Sanmartín.
0015 authors page
Shane Maureen D. Atendido and Aleli M. Ariola both graduated from Laguna State Polytechnic University with Bachelor of Secondary Education degrees specializing in mathematics. Shane finished secondary school at Balian National High School and elementary at Pangil Elementary School in Laguna province. Aleli finished secondary at Mabitac National High School and elementary at San Antonio Elementary School in Laguna province.
Apache Drill (ver. 0.2)
This document provides a high-level design proposal for Apache Drill from the OpenDremel team. It outlines four key design tenets: (1) supporting multi-tenant semantics internally without guest VMs, (2) being modular and customizable, (3) being hyper-elastic to exploit compute capacity, and (4) being efficient. It suggests an architecture with a single-tenant frontend and multi-tenant backend separated. It also provides details on the suggested designs for the frontend, CLI, REST gateway, and query compiler.
008 chapter i
This chapter discusses quadratic equations, which are equations with the highest power of the variable being 2. A quadratic equation can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. The lesson provides examples of writing equations in standard form and identifying which equations are quadratic. Students are expected to be able to identify quadratic equations, write them in standard form, and apply the distributive property when solving them.
S. Stoica - Project of Establishment of an UNESCO Centre in Physics in Romania
The SEENET-MTP Workshop JW2011
Scientific and Human Legacy of Julius Wess
27-28 August 2011, Donji Milanovac, Serbia
Search for Neutron Electric Dipole Moment
The document summarizes a proposal for a new neutron electric dipole moment (EDM) experiment at the Spallation Neutron Source (SNS). The experiment aims to improve the current neutron EDM sensitivity by two orders of magnitude using ultra-cold neutrons produced in superfluid helium-4 and polarized helium-3 as a co-magnetometer. Many feasibility studies have been conducted, including tests of the helium-3 spin precession frequency matching technique. Construction of the new neutron EDM experiment is expected to begin in fiscal year 2010 with the goal of reaching a sensitivity of less than 1×10-28 e-cm.
007 table of contents
This document outlines the table of contents for a textbook on quadratic equations and complex numbers. The textbook is divided into six chapters that cover identifying and defining quadratic equations and complex numbers, solving quadratic equations through factoring, completing the square, using the quadratic formula and graphing, solving equations in quadratic form and containing radicals, the relationship between the discriminant, roots and coefficients of quadratic equations, and solving quadratic equations using a calculator. Each chapter contains multiple lessons that delve deeper into the chapter topics.
006 general objectives
This document outlines learning objectives for a module on quadratic equations and complex numbers. Students should be able to distinguish quadratic equations from complex numbers, recognize properties of the number i, and solve quadratic equations using factoring, completing the square, quadratic formula, and graphing. Students should also be able to determine discriminants and relations between roots and coefficients, and use calculators to solve quadratic equations.
0012 chapter v
The document discusses the discriminant of quadratic equations and the relationship between the discriminant, nature of the roots, and whether the roots are real or complex. It provides examples of using the discriminant to determine if roots are real, irrational, or have multiplicity. It also explains the relationships between the sum and product of the roots of a quadratic equation and the coefficients.
0010 chapter iii
Here are the steps to solve this quadratic equation using the quadratic formula:
1. Identify the coefficients: a = 3, b = -1, c = -5/2
2. Plug the coefficients into the quadratic formula:
x = (-b ± √(b2 - 4ac)) / 2a
x = (-(-1) ± √((-1)2 - 4(3)(-5/2))) / 2(3)
3. Simplify:
x = (1 ± √(1 + 30)) / 6
4. Evaluate the square root:
x = (1 ± 5√3) / 6
Therefore, the solutions are:
0013 chapter vi
This chapter teaches students how to solve quadratic equations using a graphing calculator. It reviews solving quadratics by hand and using a calculator for basic arithmetic. Students will learn to use calculator keys to graph equations and find roots of quadratics using the quadratic formula. The document provides examples of solving quadratics step-by-step on both basic and graphing calculators. It includes a worksheet for students to practice solving 10 quadratic equations using their calculator.
0014 references
This document lists several sources that provide information about topics in algebra including: quadratic equations, polynomials, complex numbers, and their properties. Specifically, it references pages from college algebra and mathematics textbooks published between 1988 and 1992 that cover these topics. It also lists sections from a 1995 reference book on polynomials. Finally, it provides URLs for online images and information related to absolute values of complex numbers, quadratic equation coefficients, polynomial roots, and physics tools.
005 introduction
A quadratic equation is a second-order polynomial equation in one variable that takes the general form of ax^2 + bx + c, where a cannot equal 0. The constants a, b, and c are called the quadratic, linear, and constant coefficients, respectively. Quadratic equations can be solved through factoring, completing the square, graphing, using Newton's method, or the quadratic formula. This module discusses different methods for solving quadratic equations, including factoring, taking square roots, completing the square, and using the quadratic formula. It also covers identifying the discriminant and relating coefficients to roots.
009 chapter ii
The document discusses complex numbers and their arithmetic operations. It defines the imaginary unit i as the square root of -1. Complex numbers are expressed as a + bi, where a is the real part and b is the imaginary part. The four arithmetic operations of addition, subtraction, multiplication, and division are defined for complex numbers by combining or distributing real and imaginary parts. Complex numbers allow equations like x^2 + 1 = 0 to have solutions and are useful in many mathematical applications.
Dissertation Proposal
This document presents a dissertation proposal that aims to examine how simulations in high school physics classes, along with classroom management strategies, laboratory practices, student engagement techniques, critical thinking approaches, cooperative learning strategies, and teacher self-efficacy, predict student achievement. The researcher intends to survey 300 high school physics teachers who are members of the American Modeling Teachers Association and use simulations in their teaching. The survey will assess these variables and their relationship to student performance as reported by teachers. The proposal provides background research to support each variable and describes the research questions, participants, instrumentation, and data analysis plan.
Research proposal
A Research Proposal entitled “LEARNERS’ PREFERENCES AND TEACHING STRATEGIES IN TEACHING MATHEMATICS OF FOURTH YEAR HIGH SCHOOL STUDENTS AT MABITAC, LAGUNA S.Y. 2010-2011”
Viewers also liked (20)
Implantação da avaliação especial de desempenho no município de vitória
Implantação da avaliação especial de desempenho no município de vitória
S. Stoica - Project of Establishment of an UNESCO Centre in Physics in Romania
S. Stoica - Project of Establishment of an UNESCO Centre in Physics in Romania
Ptk hasil belajar fisika materi momentum dan impuls pada siswa kelas xi
Ptk hasil belajar fisika materi momentum dan impuls pada siswa kelas xi
Similar to 0011 chapter iv
Maths notes for 4038 and 4016 paper
This document provides tips for acing the Additional Mathematics (AM) and Elementary Mathematics (EM) exams. It summarizes key statistics on topics that are highly tested, such as differentiation and integration making up 27.8% of the AM exam. It recommends focusing on the 11 chapters that make up 74.6% of the exam. Sample questions are provided for topics like trigonometry, logarithms, linear laws, and matrices. Strategies are outlined for solving different types of questions on these topics.
Completing the square (added and revised)
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and explains the steps to solve quadratic equations using completing the square. These steps include: 1) moving terms to one side of the equation, 2) finding the term to complete the square and adding it to both sides, 3) factoring the perfect square trinomial, 4) taking the square root of both sides, and 5) solving for the two possible solutions. It also provides a second example where the quadratic coefficient is not 1, requiring dividing all terms by this coefficient first before completing the square.
Analytic Geometry Period 1
The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.
Ecuaciones y Desigualdades.pdf
This document provides an overview of solving linear equations, formulas, and problem solving techniques. It begins by introducing the basic properties of equality used to solve linear equations, such as distributing terms and adding/subtracting terms to isolate the variable. Examples are provided to demonstrate solving equations with fractions and solving literal equations for a specified variable. The document also discusses identities, contradictions, and using a general formula to solve families of linear equations. It concludes by outlining a problem solving guide to organize the steps of reading, visualizing, and developing an equation model to solve word problems.
5 3 solving trig eqns
To solve trigonometric equations:
1) Use standard algebraic techniques such as collecting like terms and factoring to isolate the trigonometric function.
2) Many equations are of quadratic type (ax^2 + bx + c = 0) and can be solved by factoring or using the Quadratic Formula.
3) Equations involving multiple angles (sin ku, cos ku) are first solved for ku, then divided by k.
4) Inverse trigonometric functions can be used to solve equations, with the domain restrictions of the inverse functions considered.
Module 1 topic 1 notes
This document provides an overview of solving linear equations, including:
- Slides cover solving linear equations and practice questions
- Includes an algebra cheat sheet and guide for using a graphing calculator
- Defines a linear equation and provides examples of solving linear equations algebraically by isolating the variable
- Shows checking solutions by plugging them back into the original equation
- Provides word problems applying linear equations to real-world scenarios like temperature conversion and asset depreciation
SESSION 2_COMPLETING THE SQUARE.pptx
This document discusses solving quadratic equations by completing the square. It begins by stating the objectives and key understandings of quadratic equations and the completing the square method. It then outlines the steps to complete the square, which involves rewriting the equation as a perfect square trinomial. Several examples are shown using algebra tiles and calculations. Finally, applications of completing the square to real-life problems in physics, engineering, architecture and economics are described.
Consistency of linear equations in two and three variables
This document discusses solving systems of linear equations with two or three variables. It explains that a system can have one solution, infinitely many solutions, or no solution. For two variables, the solutions are where lines intersect (one solution), coincide (infinitely many), or are parallel (no solution). For three variables, the solutions are where planes intersect (one point), lie on a line (infinitely many), or do not intersect (no solution). It demonstrates solving systems using substitution, elimination, and matrix methods, and discusses cases where a system has infinitely many or no solutions.
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
This document provides an overview of solving quadratic equations through various methods including:
- Extracting square roots to solve equations of the form x^2 = c
- Completing the square to transform equations into the form (x + b/2a)^2 = d
- Using the quadratic formula to solve any quadratic equation of the form ax^2 + bx + c = 0
It also provides strategies for determining the best approach, such as factoring if possible or using the quadratic formula if not. Examples are worked through to demonstrate each technique.
Computational skills
The document discusses different types of numbers and operations involving positive and negative numbers. It explains rules for addition, subtraction, multiplication, and division of positive and negative numbers. It also covers order of operations using PEMDAS and provides examples of solving expressions using proper order. Finally, it discusses properties and rules for exponents, including adding, subtracting, multiplying, and dividing terms with the same base and combining exponents.
.
This document provides an overview of basic algebra concepts including:
1. Variables, expressions, equations, and manipulating equations through addition, subtraction, multiplication and division while maintaining equality.
2. Solving one-variable equations by isolating the variable on one side of the equation.
3. Calculating the slope of a line using the slope-intercept form given two points on the line.
Rational Expressions Module
This document provides instruction on rational expressions. It begins with a definition of rational expressions as algebraic expressions where both the numerator and denominator are polynomials. The document then outlines the key lessons to be covered: illustrating, simplifying, and performing operations on rational expressions. Examples are provided of simplifying rational expressions by factoring and canceling common factors between the numerator and denominator. The document also demonstrates multiplying rational expressions using the same rules as multiplying fractions, as well as canceling common factors.
PRIMER GRADO ECUACIONES Y DESIGUALDADES EN UNA VARIABLE.pdf
This document provides an overview of solving first degree equations and inequalities in one variable. It defines key terms like equations, solutions, and properties of equality. It then explains the steps and properties used to solve equations with one or multiple operations, like addition, subtraction, multiplication and division. Examples are provided to demonstrate solving different types of equations and checking solutions. The document also discusses simplifying equations before solving by combining like terms.
Systems of 3 Equations in 3 Variables
The document discusses solving systems of 3 linear equations with 3 variables. It provides steps to set up the equations in standard form, eliminate one variable using two equations, eliminate the same variable from another pair of equations to get a system of 2 equations with 2 variables, solve this system to find the values of two variables, substitute these values into the original third equation to solve for the remaining variable, and check the solution. An example problem demonstrates applying these steps to solve for x, y, and z. The summary notes that the solution may not be unique depending on whether eliminating variables results in a true or false statement.
1.6 Other Types of Equations
This document provides examples and steps for solving various types of equations beyond linear equations, including:
1) Polynomial equations solved by factoring
2) Equations with radicals where radicals are eliminated by raising both sides to a power
3) Equations with rational exponents where both sides are raised to the reciprocal power
4) Equations quadratic in form where an algebraic substitution is made to transform into a quadratic equation
5) Absolute value equations where both positive and negative solutions must be considered.
Equivalent equation
Equivalent equations are equations that have the same solution sets. They are represented by the symbol "⇔". The document provides an example of equivalent equations 3x + 6 = 9 and x + 2 = 3, which have the same solution x = 3. It also discusses methods for solving equations with fractions, such as changing the equation into an equivalent equation without fractions by multiplying both sides by the lowest common multiple. Word problems can be solved by understanding the information given, representing the unknown as a variable, writing a mathematical model based on the information, solving the model, and checking the solution.
1.3 Radicals and Rational Exponents
* Evaluate square roots.
* Use the product rule to simplify square roots.
* Use the quotient rule to simplify square roots.
* Add and subtract square roots.
* Rationalize denominators.
* Use rational roots.
U3 08 ecuaciones
The document discusses equations and their definitions and classifications. It defines equality, equations, identities, variables, terms of an equation, numerical and literal equations, types of equations including polynomial, rational, radical, and absolute value equations. It provides examples of solving linear, rational, and word problems involving equations. Key steps in solving equations are outlined such as isolating the variable, using properties of equality, and verifying solutions.
MODULE_05-Matrix Decomposition.pptx
This document discusses various matrix decomposition techniques including least squares, eigendecomposition, and singular value decomposition. It begins with an introduction to the importance of linear algebra and decompositions for applications. Then it provides examples of using least squares to fit curves to data and find regression lines. It defines eigenvalues and eigenvectors and provides examples of eigendecomposition. It also discusses diagonalization of matrices and using the eigendecomposition to raise matrices to powers. Finally, it discusses singular value decomposition and its applications.
Tutorial linear equations and linear inequalities
This document discusses linear equations and inequalities in one variable. It begins by defining open sentences, variables, and solutions. It then covers topics like solving linear equations using addition, subtraction, multiplication, and division. It also discusses solving multi-step equations. Graphing solutions to equations is explained. The document also covers understanding and solving linear inequalities in one variable as well as graphing inequalities. It provides examples of how equations and inequalities can be applied to everyday situations.
Similar to 0011 chapter iv (20)
Consistency of linear equations in two and three variables
Consistency of linear equations in two and three variables
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
PRIMER GRADO ECUACIONES Y DESIGUALDADES EN UNA VARIABLE.pdf
PRIMER GRADO ECUACIONES Y DESIGUALDADES EN UNA VARIABLE.pdf
More from aleli ariola
Research problem
- The study aimed to determine the learning preferences of 4th year high school students in Mabitac, Laguna, as well as the teaching strategies used by their mathematics teachers.
- Most students were 16-year-old females from Mabitac National High School. Their top three learning preferences were visual, auditory, and kinesthetic. Teachers averaged 31 years old and had 1-5 years of experience.
- There were significant relationships between students' age, gender, and school and their learning preferences. There were also significant relationships between teachers' age, education, experience, and training and their teaching strategies. However, there was no significant relationship between students' preferences and teachers' strategies.
Field Study and Pre - Service Teaching Portfolio
This document provides information about Laguna State Polytechnic University, including its vision, mission, goals, and objectives for the Bachelor of Secondary Education program. The university aims to provide advanced education, professional, technological, and vocational instruction. Its mission is to primarily serve the Philippines and global economy. The College of Education is committed to developing students' full potential and equipping them with knowledge, skills, and attitudes for teacher education and related fields to meet changing demands. The Bachelor of Secondary Education program objectives are to produce graduates who can serve as role models, provide a wholesome learning environment, facilitate diverse learning, use various teaching methods and materials, use assessment data to improve plans, and strengthen school-community links.
Aleli powerpoint
This document discusses a study on the relationship between learners' preferences and teaching strategies in teaching mathematics to fourth year high school students in Mabitac, Laguna, Philippines. The study is guided by learning style and multiple intelligence theories. The independent variables are learners' preferences (visual, auditory, kinesthetic, analytic, global) and teaching strategies (lecture, problem solving, cooperative learning, direct teaching, indirect teaching). The dependent variable is teaching strategies. The study aims to determine the relationship between learners' preferences and teaching strategies in teaching mathematics.
Module in solving quadratic equation
________________
Date: ___________________
Instruction: Define each of the following terms:
1. Complex number
2. Real part of a complex number
3. Imaginary part of a complex number
4. Standard imaginary unit i
5. Property of i
6. Extending the real numbers
7. Solutions of an equation
8. Graph of an equation
9. X-intercepts
10. Solutions having no real numbers
11. Solutions with complex numbers
contents back next
Name: ___________________
003 forewords
This document discusses a module for solving quadratic equations that was created to fulfill the requirements of an Educational Technology course. The course introduces traditional and innovative educational technologies to help students demonstrate understanding of different technology types. Students receive guidance from faculty in selecting, producing, and using appropriate tools to develop instructional materials. By using computers and the internet, students and advisers were able to design alternative delivery systems. Creating these materials provided valuable learning experiences and the output could benefit the institution by supplementing existing instructional resources.
004 acknowledgement
The authors acknowledge and thank several people who helped them complete their educational technology module project. They thank their module adviser and computer instructor for giving them the opportunity and guidance to finish the module. They also thank their teacher consultant, previous instructor, and dean of education for their support. Finally, they thank their family, friends, and God for providing inspiration and understanding as they worked to finish the project.
002 vmgo's
Laguna State Polytechnic University aims to be a premier university in the CALABARZON region of the Philippines offering academic programs that respond to the needs of the Philippines and global economies, particularly in Asian countries. The university provides advanced education in fields like agriculture, science, engineering, teacher education, and more. It also undertakes research and community outreach. The College of Education is committed to developing students' full potential and equipping them with the knowledge, skills, and attitudes needed to be effective teachers and respond to changing times. The Bachelor of Secondary Education program aims to produce graduates who can serve as role models, provide a good learning environment, facilitate learning for diverse students, use various teaching approaches and materials, and
Module in solving quadratic equation
1. The document introduces a module on solving quadratic equations for high school students.
2. It discusses different methods for solving quadratic equations, including factoring, completing the square, using the quadratic formula, and graphing.
3. It also covers complex numbers and how to solve equations containing radicals or that can be reduced to quadratic equations.
More from aleli ariola (8)
Recently uploaded
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Building RAG with self-deployed Milvus vector database and Snowpark Container...
This talk will give hands-on advice on building RAG applications with an open-source Milvus database deployed as a docker container. We will also introduce the integration of Milvus with Snowpark Container Services.
Climate Impact of Software Testing at Nordic Testing Days
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
Full-RAG: A modern architecture for hyper-personalization
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Join us to introduce Milvus Lite, a vector database that can run on notebooks and laptops, share the same API with Milvus, and integrate with every popular GenAI framework. This webinar is perfect for developers seeking easy-to-use, well-integrated vector databases for their GenAI apps.
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
TrustArc Webinar - 2024 Global Privacy Survey
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Artificial Intelligence for XMLDevelopment
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
Video Streaming: Then, Now, and in the Future
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications.
20240605 QFM017 Machine Intelligence Reading List May 2024
Everything I found interesting about machines behaving intelligently during May 2024
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Recently uploaded (20)
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
Full-RAG: A modern architecture for hyper-personalization
Full-RAG: A modern architecture for hyper-personalization
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications
20240605 QFM017 Machine Intelligence Reading List May 2024
20240605 QFM017 Machine Intelligence Reading List May 2024
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to Production
0011 chapter iv
- 2. x2 – 3x + 2 = 0
- 3. s6 + 8s3 – 6 = 0
- 4. n2 – 6n + 10 = 0
- 7. l6 – 10l – 5 = 0
- 9. i10 – 8i5 – 4 = 0
- 11. s6 – 5s3 – 25 = 0
- 13. -349954-516441h2/4 + 8h1/4 – 12 = 0
- 15. a6- 5a4 – 15 = 0
- 17. n8 + 12n2 – 8 = 0
- 19. e9 – 3n3 – 10 = 0
- 21. x2/3 – 2x 1/3 = 8
- 24. organize the equation if it is quadratic equation; and
- 28. 3x + 4 - 5 = 0
- 29. 4x = 45
- 30. 3x - 5 = x+9
- 31. x²+15x = x + 2
- 32. Reduce to quadratic equation.
- 33. x4 – 5x + 4 = 0
- 34. 4(x + 3) + 5x+3 = 21
- 35. x2/3 – 5x1/3 – 6 = 0
- 36. (x2 + 4x)2 – (x2 + 4x) = 20
- 37. 2x4 – 9x2 + 7 = 0
- 38. Solve for x.
- 39. 6x+1 + 11-x = 2x
- 40. 1x-2 + 3x-3 + 52-x = 0
- 41. 2x+13 + 22x+1 = 53
- 42. x-1x+2 + x+3x-2 = 2
- 43. x-1x+2 + x+3x²-4 = 3x-15(x-2)