April 22, 2015
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The document discusses solving quadratic equations using the quadratic formula. It introduces the quadratic formula as -b ± √(b2 - 4ac)/2a and shows how to use it to solve various quadratic equations by identifying the a, b, and c coefficients and plugging them into the formula. Examples are provided to demonstrate solving equations step-by-step using the quadratic formula.
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April 15, 2014
The document provides instruction on solving quadratic equations using the quadratic formula. It introduces the quadratic formula as the ultimate method for solving all quadratic equations, including those deemed previously "unsolvable". The formula is presented as ax^2 + bx + c = 0, and students are walked through examples of plugging values into the formula and solving for x. While the quadratic formula can solve all quadratic equations, it requires memorizing the formula and being careful with signs and order of operations.
Factoring perfect square trinomials
This document discusses factoring perfect square trinomials. It defines a perfect square trinomial as one where the first and last terms are squares of the same variable and the middle term is twice the product of the variables in the first and last terms. The document provides the formulas for factoring perfect square trinomials that are the sum or difference of squares. It includes an example problem set that factors three perfect square trinomials. The document assesses the student's ability to factor perfect square trinomials through a performance task and assessment task.
1.5 comparison statements, inequalities and intervals t
This document discusses comparison statements, inequalities, and intervals. It defines positive and negative numbers, comparative statements like greater than and less than, and inequality notations like x < c. It introduces interval notation for ranges of values like [a,b] and operations on intervals like union and intersection. Examples are provided to illustrate translating between inequality statements and geometric representations. Exercises involve drawing inequalities, translating between phrases and notations, evaluating interval expressions, and expressing absolute value inequalities in interval form.
16.6 Quadratic Formula & Discriminant
The document discusses solving quadratic equations using the quadratic formula. It defines the discriminant as the expression under the radical sign in the quadratic formula, and explains that the discriminant determines the number of real roots: a positive discriminant means two real roots, zero discriminant means one real root, and a negative discriminant means no real roots. Examples are provided to demonstrate solving quadratic equations using the quadratic formula and interpreting the discriminant.
Quadratic Formula
The document discusses solving quadratic equations using the quadratic formula. It provides the general form of a quadratic equation as ax2 + bx + c = 0 and introduces the quadratic formula as x = (-b ± √(b2 - 4ac))/2a. Several examples of using the quadratic formula to solve quadratic equations are shown step-by-step with explanations of each step. The examples illustrate determining the a, b, and c coefficients and performing the calculations to find the roots of the equations.
solving quadratic equations using quadratic formula
The document discusses how to use the quadratic formula to solve quadratic equations. It provides the formula: x = (-b ± √(b2 - 4ac)) / 2a. It then works through examples of writing quadratic equations in standard form (ax2 + bx + c = 0) and using the formula to solve them. Specifically, it solves the equations: 1) 1x2 + 3x - 27 = 0, 2) 2x2 + 7x + 5 = 0, 3) x2 - 2x = 8, and 4) x2 - 7x = 10. It concludes by providing 3 additional equations to solve using the quadratic formula.
Applications of Quadratic Equations and Rational Algebraic Equations
Provides example and solutions on solving problems involving quadratic equations and rational algebraic equation.
Solving Quadratic Equations
Provides example on how to solve quadratic equations using extracting square roots, factoring, completing the square and quadratic formula.
Recommended
April 15, 2014
The document provides instruction on solving quadratic equations using the quadratic formula. It introduces the quadratic formula as the ultimate method for solving all quadratic equations, including those deemed previously "unsolvable". The formula is presented as ax^2 + bx + c = 0, and students are walked through examples of plugging values into the formula and solving for x. While the quadratic formula can solve all quadratic equations, it requires memorizing the formula and being careful with signs and order of operations.
Factoring perfect square trinomials
This document discusses factoring perfect square trinomials. It defines a perfect square trinomial as one where the first and last terms are squares of the same variable and the middle term is twice the product of the variables in the first and last terms. The document provides the formulas for factoring perfect square trinomials that are the sum or difference of squares. It includes an example problem set that factors three perfect square trinomials. The document assesses the student's ability to factor perfect square trinomials through a performance task and assessment task.
1.5 comparison statements, inequalities and intervals t
This document discusses comparison statements, inequalities, and intervals. It defines positive and negative numbers, comparative statements like greater than and less than, and inequality notations like x < c. It introduces interval notation for ranges of values like [a,b] and operations on intervals like union and intersection. Examples are provided to illustrate translating between inequality statements and geometric representations. Exercises involve drawing inequalities, translating between phrases and notations, evaluating interval expressions, and expressing absolute value inequalities in interval form.
16.6 Quadratic Formula & Discriminant
The document discusses solving quadratic equations using the quadratic formula. It defines the discriminant as the expression under the radical sign in the quadratic formula, and explains that the discriminant determines the number of real roots: a positive discriminant means two real roots, zero discriminant means one real root, and a negative discriminant means no real roots. Examples are provided to demonstrate solving quadratic equations using the quadratic formula and interpreting the discriminant.
Quadratic Formula
The document discusses solving quadratic equations using the quadratic formula. It provides the general form of a quadratic equation as ax2 + bx + c = 0 and introduces the quadratic formula as x = (-b ± √(b2 - 4ac))/2a. Several examples of using the quadratic formula to solve quadratic equations are shown step-by-step with explanations of each step. The examples illustrate determining the a, b, and c coefficients and performing the calculations to find the roots of the equations.
solving quadratic equations using quadratic formula
The document discusses how to use the quadratic formula to solve quadratic equations. It provides the formula: x = (-b ± √(b2 - 4ac)) / 2a. It then works through examples of writing quadratic equations in standard form (ax2 + bx + c = 0) and using the formula to solve them. Specifically, it solves the equations: 1) 1x2 + 3x - 27 = 0, 2) 2x2 + 7x + 5 = 0, 3) x2 - 2x = 8, and 4) x2 - 7x = 10. It concludes by providing 3 additional equations to solve using the quadratic formula.
Applications of Quadratic Equations and Rational Algebraic Equations
Provides example and solutions on solving problems involving quadratic equations and rational algebraic equation.
Solving Quadratic Equations
Provides example on how to solve quadratic equations using extracting square roots, factoring, completing the square and quadratic formula.
Bca3010 computer oriented numerical methods
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
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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.
Solving Quadratic Equations by Completing the Square
For more instructional resources, CLICK me here!
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https://tinyurl.com/ycjp8r7u
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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.
quadratic equation
The document provides information about quadratic equations including:
1) It defines a quadratic equation as a polynomial equation of the second degree in the form ax2 + bx + c, where a ≠ 0. The constants a, b, and c are the quadratic, linear, and constant coefficients.
2) There are three main methods to solve quadratic equations: factoring, completing the square, or using the quadratic formula.
3) The discriminant, b2 - 4ac, determines the nature of the roots - two real roots if positive, one real root if zero, or two complex roots if negative.
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 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 functions my maths presentation
1. The document discusses key concepts related to quadratic equations including factorizing, solving, graphing, finding roots and axis of symmetry, locating maximum/minimum values, and using graphs to solve related equations and inequalities.
2. The key steps provided to factorize a quadratic equation are to find the product and factors of the coefficients that add up to the middle term, and then pair the factors.
3. To solve a quadratic equation, take all terms to one side, factorize, set each factor equal to 0 and solve for x to find the two roots.
Core 3 Modulus 2
The document discusses solving simple modulus equations by setting the expressions equal and solving, either by isolating the variable or squaring both sides. It provides examples of solving equations of the form |ax + b| = c and |ax + b| = |cx + d|. The examples show setting the expressions equal, isolating the variable, and finding the solutions, or squaring both sides to remove the modulus and then solving the resulting equation.
16.2 Solving by Factoring
This document provides an overview of solving quadratic equations by factoring. It begins with the standard form of a quadratic equation and explains the zero factor property. Examples are provided to demonstrate factoring quadratic equations and setting each factor equal to zero to solve. The steps for solving a quadratic equation by factoring are outlined. Additional examples demonstrate solving real world application problems involving quadratic equations.
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 Form 1-Chapter 3 Squares, Square Roots, Cubes and Cube Roots KBSM...
1. Squares are the product of a number multiplied by itself. Squares of fractions, decimals, and negative numbers can be calculated using this property.
2. Perfect squares are numbers that are the result of squaring another number. Prime factorization can help determine if a number is a perfect square.
3. The document provides examples of calculating squares and identifying perfect squares, and includes practice exercises for working with squares.
1.3 solving equations t
1. The document discusses various methods for solving different types of equations including: polynomial equations using factoring, quadratic equations using the quadratic formula, rational equations by clearing denominators, radical equations by squaring both sides, and absolute value equations geometrically.
2. Specific examples are provided to demonstrate how to solve equations involving polynomials, rationals, radicals, powers, and absolute values. Steps include factoring, using the quadratic formula, clearing denominators, isolating and squaring radicals, and raising both sides to appropriate powers.
3. The document also discusses finding zeros of rational functions and domains by determining where the numerator or denominator is equal to zero.
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.
16.1 Solving Quadratics by square roots
This document introduces the square root property and method for solving quadratic equations using square roots. It provides 3 steps: 1) isolate the term being squared, 2) take the square root of both sides, and 3) solve the remaining equation if needed. Examples are shown of solving equations of the form x^2=a, (x-b)^2=c, and (ax-b)^2=c by taking the square root and solving the resulting linear equations. It is noted that some quadratic equations using this method may have no real solutions.
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.
Factoring Perfect Square Trinomial - SIM
This document contains information and examples about perfect square trinomials in algebra. It defines a perfect square trinomial as having a first term and last term that are perfect squares, with a middle term that is twice the product of the square roots of the first and last terms. Examples are provided to illustrate how to identify if an expression is a perfect square trinomial or not. Several activity cards are included that provide practice identifying, factoring, and giving the factors of perfect square trinomial expressions.
Solving Word Problems Involving Quadratic Equations
This document provides instructions for solving word problems involving quadratic equations. It explains how to write let statements and equations, solve for consecutive integers or areas, and check solutions. Sample problems are worked through, such as finding two consecutive integers whose sum is 13, or the dimensions of a rectangular garden with an area of 27 square units.
Factoring Quadratic Trinomials
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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.
We .jpg
Morphology is the study of word formation and interpretation. It examines how words are established through morphemes and how compound words are varied in a language. There are free morphemes that can stand alone with meaning, and bound morphemes that cannot. Function morphemes include inflection morphemes that change words to be additive without changing meaning. Word formation processes include borrowing words from other languages and coining new words without regard to typical formation rules. Studying morphology deepens understanding of word structure and provides knowledge of proper language use through understanding morpheme types and principles.
MINERIA DE DATOS
El documento habla sobre la minería de datos y su utilidad. Explica que la minería de datos es el proceso de análisis de grandes cantidades de datos para identificar patrones útiles. También describe cómo la minería de datos se ha aplicado en diversos campos como el comercio minorista, la medicina, la astronomía y más, para apoyar la toma de decisiones mediante el estudio de grandes conjuntos de datos.
More Related Content
What's hot
Bca3010 computer oriented numerical methods
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
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.
Solving Quadratic Equations by Completing the Square
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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.
quadratic equation
The document provides information about quadratic equations including:
1) It defines a quadratic equation as a polynomial equation of the second degree in the form ax2 + bx + c, where a ≠ 0. The constants a, b, and c are the quadratic, linear, and constant coefficients.
2) There are three main methods to solve quadratic equations: factoring, completing the square, or using the quadratic formula.
3) The discriminant, b2 - 4ac, determines the nature of the roots - two real roots if positive, one real root if zero, or two complex roots if negative.
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 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 functions my maths presentation
1. The document discusses key concepts related to quadratic equations including factorizing, solving, graphing, finding roots and axis of symmetry, locating maximum/minimum values, and using graphs to solve related equations and inequalities.
2. The key steps provided to factorize a quadratic equation are to find the product and factors of the coefficients that add up to the middle term, and then pair the factors.
3. To solve a quadratic equation, take all terms to one side, factorize, set each factor equal to 0 and solve for x to find the two roots.
Core 3 Modulus 2
The document discusses solving simple modulus equations by setting the expressions equal and solving, either by isolating the variable or squaring both sides. It provides examples of solving equations of the form |ax + b| = c and |ax + b| = |cx + d|. The examples show setting the expressions equal, isolating the variable, and finding the solutions, or squaring both sides to remove the modulus and then solving the resulting equation.
16.2 Solving by Factoring
This document provides an overview of solving quadratic equations by factoring. It begins with the standard form of a quadratic equation and explains the zero factor property. Examples are provided to demonstrate factoring quadratic equations and setting each factor equal to zero to solve. The steps for solving a quadratic equation by factoring are outlined. Additional examples demonstrate solving real world application problems involving quadratic equations.
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 Form 1-Chapter 3 Squares, Square Roots, Cubes and Cube Roots KBSM...
1. Squares are the product of a number multiplied by itself. Squares of fractions, decimals, and negative numbers can be calculated using this property.
2. Perfect squares are numbers that are the result of squaring another number. Prime factorization can help determine if a number is a perfect square.
3. The document provides examples of calculating squares and identifying perfect squares, and includes practice exercises for working with squares.
1.3 solving equations t
1. The document discusses various methods for solving different types of equations including: polynomial equations using factoring, quadratic equations using the quadratic formula, rational equations by clearing denominators, radical equations by squaring both sides, and absolute value equations geometrically.
2. Specific examples are provided to demonstrate how to solve equations involving polynomials, rationals, radicals, powers, and absolute values. Steps include factoring, using the quadratic formula, clearing denominators, isolating and squaring radicals, and raising both sides to appropriate powers.
3. The document also discusses finding zeros of rational functions and domains by determining where the numerator or denominator is equal to zero.
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.
16.1 Solving Quadratics by square roots
This document introduces the square root property and method for solving quadratic equations using square roots. It provides 3 steps: 1) isolate the term being squared, 2) take the square root of both sides, and 3) solve the remaining equation if needed. Examples are shown of solving equations of the form x^2=a, (x-b)^2=c, and (ax-b)^2=c by taking the square root and solving the resulting linear equations. It is noted that some quadratic equations using this method may have no real solutions.
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.
Factoring Perfect Square Trinomial - SIM
This document contains information and examples about perfect square trinomials in algebra. It defines a perfect square trinomial as having a first term and last term that are perfect squares, with a middle term that is twice the product of the square roots of the first and last terms. Examples are provided to illustrate how to identify if an expression is a perfect square trinomial or not. Several activity cards are included that provide practice identifying, factoring, and giving the factors of perfect square trinomial expressions.
Solving Word Problems Involving Quadratic Equations
This document provides instructions for solving word problems involving quadratic equations. It explains how to write let statements and equations, solve for consecutive integers or areas, and check solutions. Sample problems are worked through, such as finding two consecutive integers whose sum is 13, or the dimensions of a rectangular garden with an area of 27 square units.
Factoring Quadratic Trinomials
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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.
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Morphology is the study of word formation and interpretation. It examines how words are established through morphemes and how compound words are varied in a language. There are free morphemes that can stand alone with meaning, and bound morphemes that cannot. Function morphemes include inflection morphemes that change words to be additive without changing meaning. Word formation processes include borrowing words from other languages and coining new words without regard to typical formation rules. Studying morphology deepens understanding of word structure and provides knowledge of proper language use through understanding morpheme types and principles.
MINERIA DE DATOS
El documento habla sobre la minería de datos y su utilidad. Explica que la minería de datos es el proceso de análisis de grandes cantidades de datos para identificar patrones útiles. También describe cómo la minería de datos se ha aplicado en diversos campos como el comercio minorista, la medicina, la astronomía y más, para apoyar la toma de decisiones mediante el estudio de grandes conjuntos de datos.
March 3, 2015
Tomorrow there will be a scientific notation test covering converting numbers between standard and scientific notation, multiplying and dividing with scientific notation, and word problems involving scientific notation and systems of equations. The document provides a list of topics and number of questions for each topic that will be on the test. It also provides reminders about using a pencil instead of a pen, having the correct code for the test, and that scratch paper but no phones will be allowed.
March 13, 2015
The document provides an agenda for a student's school day which includes:
1) Checking equipment and doing mental stretches before a pre-game warm up and game time where they will review their game plan.
2) A math test review covering perimeter and area formulas, factoring quadratic expressions, and solving quadratic equations.
3) Instructions for the math test emphasizing having only a pencil, scratch paper and guidelines at their desk along with correctly bubbling their student code for full credit. The test is their last chance to earn a 3.8 GPA.
Dr Yousef Elshrek is One co-authors in this study >>>> Global, regional, and...
Global, regional, and national age–sex specifi c all-cause and cause-specifi c mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013
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On designing automatic reaction strategy for critical infrastructure scada sy...
On designing automatic reaction strategy for critical infrastructure scada sy...Luxembourg Institute of Science and Technology
This document proposes an automatic reaction strategy for critical infrastructure SCADA systems. It defines a three-layer metamodel for modeling SCADA components and two types of policies (cognitive and permissive) that govern component behavior. It then presents a two-phase method for identifying these policies from the SCADA architecture and formalizing them to support an automatic reaction strategy. This strategy is modeled as an integral part of the SCADA architecture using the defined metamodel and policy identification method. It includes organizational and application layers with main actors, strategies, and components that realize the reaction policies based on expected automation levels.Eric Jordan at Solespace 2015
Eric Jordan held a solo art show titled "Sole Space" in 2015. The show featured Eric Jordan's artwork and was a solo exhibition for the artist. It took place in 2015 and was titled "Sole Space".
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Dr Yousef Elshrek is One co-authors in this study >>>> Global, regional, and...
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April 22, 2015
- 1. SOLVING QUADRATIC EQUATIONS April 22, 2015 USING THE QUADRATIC FORMULA
- 2. WARM-UP
- 3. You now possess 5 methods to solve quadratic equations. They are: C) Finding square rootsB) Completing the square D) Creating a table of x/y values A) Factoring And now, an important rite of passage from child to adult, You are to receive the ultimate weapon in the quadratic wars. With this, you can replace A-D above with this single method, Presenting.. E) Graphing
- 4. −𝑏 ± 𝑏2 − 4𝑎𝑐 2𝑎 **She’s beautiful, and she’s all yours *The Quadratic Formula:
- 5. THE QUADRATIC FORMULA .....Solves every quadratic equation, making ‘unsolvable’ a thing of the past. However, some quadratics, such as x = −𝟏 are solved with i, imaginary numbers. Pro’s Cons No figuring out what method to use Formula must be memorized If used every time, solving will be easier and faster Must always be aware of signs and order of operations
- 6. The first thing we need to do is to see if this fits the first formula. It does since it has the variable squared, the coefficient and the constant all equaling to zero. Next we find the a, b & c and put them into the second formula. a = 2 b = -5 c = -3 SOLVE EQUATIONS WITH THE QUADRATIC FORMULA 2x2 – 5x – 3 = 0
- 7. EXAMPLE 1 x = 5 + 7 4 x = 12 4 x = 5 - 7 4 x = -2 4 x = 3 x = -1/2
- 8. Rearrange to standard form first EXAMPLE 2 Solve 2x2 + 7x = 9 2x2 + 7x – 9 = 0 Identify the a, b & c and plug them in. 2x2 + 7x – 9 = 0
- 9. Now we identify the a, b & c and place it in formula two. Then we solve. x = -(7) ± √(7)2 – 4(2)(-9) 2(2) x = -7 ± √49 – (- 72) 4 x = -7 ± √121 4 x = -7 ± 11 4 EXAMPLE 2
- 10. x = -7 ± 11 4 x = 4 4 x = 1 x = -9/2 EXAMPLE 2 x = -7 - 11 4 x = -18 4 x = -7 + 11 4
- 11. x = -(1) ± √(1)2 – 4(1)(-1) 2(1) LAST EXAMPLE Solve x2 + x – 1 = 0 First we need to identify a, b & c
- 12. x = -(1) ± √(1)2 – 4(1)(-1) 2(1) We can go no further since 5 can’t be squared. x = -1 + √5 2 x = -1 - √5 2 x = -1 ± √5 2 x = -1 ± √1+ 4 2 LAST EXAMPLE
- 13. BACK TO OUR FIRST “UNSOLVABLE” QUADRATIC EQUATION TODAY: 5x2 + 3x + 12
- 14. COMPLETE & SUBMIT CLASS WORK TODAY!