Lesson graphing using intercepts
•Download as PPTX, PDF•
2 likes•1,560 views
This document provides an explanation and examples of using intercepts to graph linear equations. It defines x-intercept as the x-coordinate where the graph crosses the x-axis and y-intercept as the y-coordinate where the graph crosses the y-axis. Examples are given of finding intercepts of equations by setting either x or y to 0 and then solving for the other variable. The intercepts are then used to graph the line.
Report
Share
Report
Share
Recommended
11.2 graphing linear equations in two variables
The document discusses how to graph linear equations and inequalities in two variables. It provides examples of graphing linear equations by plotting ordered pairs, finding intercepts, and using linear equations to model data. Specifically, it shows how to graph equations of the form y=mx+b, Ax+By=0, y=b, and x=a. It demonstrates finding intercepts and using them to graph equations. Finally, it gives an example of using a linear equation to model the monthly costs of a small business based on the number of products sold.
Adding Polynomials
This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.
Division Of Polynomials
Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.
Adding and subtracting polynomials
Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
Domain and range
The document discusses domain and range of graphs. It defines domain as all the x-values and range as all the y-values of a graph. It provides examples of determining the domain and range from graphs, describing whether they include or exclude endpoint values and how to write the domain and range in inequality notation.
Factoring Sum and Difference of Two Cubes
This will help you in factoring sum and difference of two cubes.
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 quadratics by completing the square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.
Addition and subtraction of rational expression
To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.
Recommended
11.2 graphing linear equations in two variables
The document discusses how to graph linear equations and inequalities in two variables. It provides examples of graphing linear equations by plotting ordered pairs, finding intercepts, and using linear equations to model data. Specifically, it shows how to graph equations of the form y=mx+b, Ax+By=0, y=b, and x=a. It demonstrates finding intercepts and using them to graph equations. Finally, it gives an example of using a linear equation to model the monthly costs of a small business based on the number of products sold.
Adding Polynomials
This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.
Division Of Polynomials
Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.
Adding and subtracting polynomials
Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variables and the same exponents. To add polynomials, terms are grouped by their like terms and the coefficients are combined by adding them. To subtract polynomials, the process is the same as adding the opposite of the second polynomial. The opposite of each term is found by changing its sign. Then the like terms are combined in the same way as when adding.
Domain and range
The document discusses domain and range of graphs. It defines domain as all the x-values and range as all the y-values of a graph. It provides examples of determining the domain and range from graphs, describing whether they include or exclude endpoint values and how to write the domain and range in inequality notation.
Factoring Sum and Difference of Two Cubes
This will help you in factoring sum and difference of two cubes.
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 quadratics by completing the square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.
Addition and subtraction of rational expression
To add or subtract fractions with unlike denominators:
1. Find the least common denominator (LCD), which contains all prime factors of each denominator raised to the highest power.
2. Convert the fractions to equivalent fractions with the LCD as the denominator.
3. Perform the addition or subtraction on the numerators and write the sum or difference over the common denominator.
Inequalities ppt revised
Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
-14 -14
m < -10
Graph: m < -10
2) -7 > y-1
+1 +1
-6 > y
y < -6
Graph: y < -6
3) (-3)k < 10(-3)
-3
k > -30
Graph: k > -30
4) 2x + 5 ≤ x + 1
-x -x
x + 5 ≤ 1
-5 -5
x ≤ -4
Graph: x ≤ -4
Parts of quadratic function and transforming to general form to vertex form a...
This document contains notes and materials for a Math 9 class covering quadratic functions for the 6th week of the 1st quarter. It includes:
1. A math prayer to work problems and trust in God's help.
2. An overview of topics to be covered: illustrating quadratic functions, transforming between general and vertex forms, and determining parts of quadratic graphs.
3. A review question asking students to identify which situation represents a quadratic function.
4. Examples of transforming between the general and vertex forms of quadratic functions.
5. Key parts of graphs of quadratic functions including the vertex, axis of symmetry, x- and y-intercepts, and the effect of the leading coefficient on
Quadratic function
The document discusses quadratic functions and their zeros. It provides examples of finding the zeros of quadratic functions by factoring, completing the square, and using the quadratic formula. It also gives examples of writing the equation of a quadratic function given its zeros or given properties like the vertex and y-intercept. Methods discussed include using the fact that the zeros are the roots of the corresponding equation, and substituting known point values into the quadratic formula.
Factoring Trinomials
This document provides a step-by-step algorithm for factoring second degree trinomials in an organized manner. The algorithm involves multiplying the leading coefficient and constant term, finding factors that add to the coefficient of the linear term, rewriting the trinomial by replacing the linear term, grouping pairs of terms, factoring out the greatest common factor of each pair, factoring out the common binomial, and writing the fully factored trinomial. Following these steps takes much of the guesswork out of factoring trinomials.
Properties of logarithms
This document discusses properties of logarithms, including:
1) Logarithms with the same base "undo" each other according to the inverse function relationship between logarithms and exponents.
2) Logarithmic expressions can be expanded using properties to write them as sums or differences of individual logarithmic terms, or condensed into a single logarithm.
3) The change of base formula allows converting between logarithms with different bases, with common uses being to change to base 10 or the base of natural logarithms.
Factoring Quadratic Trinomials
The document provides instructions for factoring quadratic trinomials using 4 examples. It explains that you write the trinomial as two parentheses, factor the constant term into the parentheses, then check that the factors give the middle term of the original expression when multiplied out. The process involves 4 steps and is demonstrated factoring expressions like x^2 + 10x + 24 and x^2 - 8x + 15.
Total Surface Area of Prisms
The document discusses calculating the total surface area (TSA) of different 3D shapes by unfolding them into their 2D nets. It provides the TSA formulas and worked examples for rectangular prisms, triangular prisms, cylinders, and square pyramids. Engineers, builders and others use TSA to determine material needs like paint or carpet for projects. The document emphasizes that TSA is an area measurement, not a volume.
QUADRATIC FUNCTIONS
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
Logarithmic Functions
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
Multiplication of polynomials
The document discusses multiplying polynomials, including multiplying monomials, combining like terms, and special cases such as the sum and difference of binomials, squares of binomials, and cubes of binomials. Examples are provided for multiplying polynomials with 2, 3, or 4 terms. Formulas and step-by-step workings are shown for finding products of binomial expressions.
Factoring Perfect Square 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
Exponential and logarithmic functions
This document provides an overview of exponential and logarithmic functions. It defines one-to-one functions and inverse functions. It explains how to find the inverse of a one-to-one function and shows that the inverse of f(x) is f-1(x). Properties of exponential functions like f(x)=ax and logarithmic functions like f(x)=logax are described. The product, quotient, and power rules for logarithms are outlined along with examples. Finally, it discusses how to solve exponential and logarithmic equations using properties of these functions.
Solving Quadratic Equations by Factoring
The document discusses solving quadratic equations by factoring. It provides examples of factoring quadratic expressions to find the solutions to the equations. These include using the zero product rule, factoring a common factor, and factoring a perfect square. It also provides two word problems involving consecutive integers and the Pythagorean theorem and shows how to set up and solve the quadratic equations derived from the word problems.
Chapter 5 Slope-Intercept Form
This document provides a lesson on writing and graphing linear equations in slope-intercept form. It begins with examples of finding the slope and y-intercept of lines and writing the equation in the form y = mx + b. Then it shows how to graph lines from their equations in slope-intercept form. Applications include writing cost functions and finding values. A quiz reviews writing equations from slopes and points and graphing lines from their equations.
Rational Expressions
To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.
Cube of binomial
The cube of a binomial can be found using the formula F3 + 3F2L + 3FL2 + L3, where:
- F3 is the cube of the first term
- 3F2L is 3 times the square of the first term multiplied by the second term
- 3FL2 is 3 times the first term multiplied by the square of the second term
- L3 is the cube of the second term
This formula is demonstrated through examples of finding the cubes of (x + 2), (x - 2), and (2x + y).
7-1 Graphing Exponential Functions - modified for online.pptx
1. The document discusses graphing exponential functions by completing tables of values for functions like y=3^x and y=2x+1, and plotting the points on a graph. It covers exponential growth and decay functions.
2. Examples show how to graph transformed exponential functions with additions or multiplications like y=2x+1, which has a horizontal asymptote at y=1.
3. Practice problems provide more opportunities to complete tables of values and graph exponential functions, including those with horizontal asymptotes.
Multiplying polynomials
This document discusses multiplying polynomials. It begins with examples of multiplying monomials by using the properties of exponents. It then covers multiplying a polynomial by a monomial using the distributive property. Examples are provided for multiplying binomials by binomials using both the distributive property and FOIL method. The document concludes by explaining methods for multiplying polynomials with more than two terms, such as using the distributive property multiple times, a rectangle model, or a vertical method similar to multiplying whole numbers.
Factoring Polynomials
This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.
Distance formula
This document explains the distance formula and how to use it to calculate the distance between points on a Cartesian plane. It provides the steps to use the Pythagorean theorem to derive the distance formula: take the difference between the x-coordinates squared and add it to the difference between the y-coordinates squared, and take the square root of the result. It then works through an example of using the distance formula to calculate the distance between points (3,2) and (8,7), which equals 5 units. The document concludes with practice problems and assignments applying the distance formula.
Intercepts
This document explains how to find the x-intercept and y-intercept of a graph from its equation. The x-intercept is where the graph crosses the x-axis and is of the form (x,0), while the y-intercept is where the graph crosses the y-axis and is of the form (0,y). To find the x-intercept, set y=0 and solve for x; to find the y-intercept, set x=0 and solve for y. Examples are provided finding the intercepts of equations by setting variables equal to 0 and solving.
Topic 4 solving quadratic equations part 1
This document provides instruction on solving quadratic equations. It begins with an introduction to quadratic equations and examples of their real-world applications. It then presents several examples of solving quadratic equations by factoring and setting each factor equal to 0. Various methods are demonstrated including solving by factoring trinomials and binomials. Finally, students are provided practice problems to solve quadratic equations on their own.
More Related Content
What's hot
Inequalities ppt revised
Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
-14 -14
m < -10
Graph: m < -10
2) -7 > y-1
+1 +1
-6 > y
y < -6
Graph: y < -6
3) (-3)k < 10(-3)
-3
k > -30
Graph: k > -30
4) 2x + 5 ≤ x + 1
-x -x
x + 5 ≤ 1
-5 -5
x ≤ -4
Graph: x ≤ -4
Parts of quadratic function and transforming to general form to vertex form a...
This document contains notes and materials for a Math 9 class covering quadratic functions for the 6th week of the 1st quarter. It includes:
1. A math prayer to work problems and trust in God's help.
2. An overview of topics to be covered: illustrating quadratic functions, transforming between general and vertex forms, and determining parts of quadratic graphs.
3. A review question asking students to identify which situation represents a quadratic function.
4. Examples of transforming between the general and vertex forms of quadratic functions.
5. Key parts of graphs of quadratic functions including the vertex, axis of symmetry, x- and y-intercepts, and the effect of the leading coefficient on
Quadratic function
The document discusses quadratic functions and their zeros. It provides examples of finding the zeros of quadratic functions by factoring, completing the square, and using the quadratic formula. It also gives examples of writing the equation of a quadratic function given its zeros or given properties like the vertex and y-intercept. Methods discussed include using the fact that the zeros are the roots of the corresponding equation, and substituting known point values into the quadratic formula.
Factoring Trinomials
This document provides a step-by-step algorithm for factoring second degree trinomials in an organized manner. The algorithm involves multiplying the leading coefficient and constant term, finding factors that add to the coefficient of the linear term, rewriting the trinomial by replacing the linear term, grouping pairs of terms, factoring out the greatest common factor of each pair, factoring out the common binomial, and writing the fully factored trinomial. Following these steps takes much of the guesswork out of factoring trinomials.
Properties of logarithms
This document discusses properties of logarithms, including:
1) Logarithms with the same base "undo" each other according to the inverse function relationship between logarithms and exponents.
2) Logarithmic expressions can be expanded using properties to write them as sums or differences of individual logarithmic terms, or condensed into a single logarithm.
3) The change of base formula allows converting between logarithms with different bases, with common uses being to change to base 10 or the base of natural logarithms.
Factoring Quadratic Trinomials
The document provides instructions for factoring quadratic trinomials using 4 examples. It explains that you write the trinomial as two parentheses, factor the constant term into the parentheses, then check that the factors give the middle term of the original expression when multiplied out. The process involves 4 steps and is demonstrated factoring expressions like x^2 + 10x + 24 and x^2 - 8x + 15.
Total Surface Area of Prisms
The document discusses calculating the total surface area (TSA) of different 3D shapes by unfolding them into their 2D nets. It provides the TSA formulas and worked examples for rectangular prisms, triangular prisms, cylinders, and square pyramids. Engineers, builders and others use TSA to determine material needs like paint or carpet for projects. The document emphasizes that TSA is an area measurement, not a volume.
QUADRATIC FUNCTIONS
The document provides an overview of quadratic functions including definitions of key terms like quadratic function, parabola, quadratic equation, and vertex form. It discusses how to graph quadratic functions, solve quadratic equations using methods like the quadratic formula, and find the maximums and minimums of quadratic functions. It includes examples of using these techniques to solve word problems involving quadratic applications. The document aims to teach students about the basic concepts of quadratic functions.
Logarithmic Functions
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
Multiplication of polynomials
The document discusses multiplying polynomials, including multiplying monomials, combining like terms, and special cases such as the sum and difference of binomials, squares of binomials, and cubes of binomials. Examples are provided for multiplying polynomials with 2, 3, or 4 terms. Formulas and step-by-step workings are shown for finding products of binomial expressions.
Factoring Perfect Square 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
Exponential and logarithmic functions
This document provides an overview of exponential and logarithmic functions. It defines one-to-one functions and inverse functions. It explains how to find the inverse of a one-to-one function and shows that the inverse of f(x) is f-1(x). Properties of exponential functions like f(x)=ax and logarithmic functions like f(x)=logax are described. The product, quotient, and power rules for logarithms are outlined along with examples. Finally, it discusses how to solve exponential and logarithmic equations using properties of these functions.
Solving Quadratic Equations by Factoring
The document discusses solving quadratic equations by factoring. It provides examples of factoring quadratic expressions to find the solutions to the equations. These include using the zero product rule, factoring a common factor, and factoring a perfect square. It also provides two word problems involving consecutive integers and the Pythagorean theorem and shows how to set up and solve the quadratic equations derived from the word problems.
Chapter 5 Slope-Intercept Form
This document provides a lesson on writing and graphing linear equations in slope-intercept form. It begins with examples of finding the slope and y-intercept of lines and writing the equation in the form y = mx + b. Then it shows how to graph lines from their equations in slope-intercept form. Applications include writing cost functions and finding values. A quiz reviews writing equations from slopes and points and graphing lines from their equations.
Rational Expressions
To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.
Cube of binomial
The cube of a binomial can be found using the formula F3 + 3F2L + 3FL2 + L3, where:
- F3 is the cube of the first term
- 3F2L is 3 times the square of the first term multiplied by the second term
- 3FL2 is 3 times the first term multiplied by the square of the second term
- L3 is the cube of the second term
This formula is demonstrated through examples of finding the cubes of (x + 2), (x - 2), and (2x + y).
7-1 Graphing Exponential Functions - modified for online.pptx
1. The document discusses graphing exponential functions by completing tables of values for functions like y=3^x and y=2x+1, and plotting the points on a graph. It covers exponential growth and decay functions.
2. Examples show how to graph transformed exponential functions with additions or multiplications like y=2x+1, which has a horizontal asymptote at y=1.
3. Practice problems provide more opportunities to complete tables of values and graph exponential functions, including those with horizontal asymptotes.
Multiplying polynomials
This document discusses multiplying polynomials. It begins with examples of multiplying monomials by using the properties of exponents. It then covers multiplying a polynomial by a monomial using the distributive property. Examples are provided for multiplying binomials by binomials using both the distributive property and FOIL method. The document concludes by explaining methods for multiplying polynomials with more than two terms, such as using the distributive property multiple times, a rectangle model, or a vertical method similar to multiplying whole numbers.
Factoring Polynomials
This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.
Distance formula
This document explains the distance formula and how to use it to calculate the distance between points on a Cartesian plane. It provides the steps to use the Pythagorean theorem to derive the distance formula: take the difference between the x-coordinates squared and add it to the difference between the y-coordinates squared, and take the square root of the result. It then works through an example of using the distance formula to calculate the distance between points (3,2) and (8,7), which equals 5 units. The document concludes with practice problems and assignments applying the distance formula.
What's hot (20)
Parts of quadratic function and transforming to general form to vertex form a...
Parts of quadratic function and transforming to general form to vertex form a...
7-1 Graphing Exponential Functions - modified for online.pptx
7-1 Graphing Exponential Functions - modified for online.pptx
Similar to Lesson graphing using intercepts
Intercepts
This document explains how to find the x-intercept and y-intercept of a graph from its equation. The x-intercept is where the graph crosses the x-axis and is of the form (x,0), while the y-intercept is where the graph crosses the y-axis and is of the form (0,y). To find the x-intercept, set y=0 and solve for x; to find the y-intercept, set x=0 and solve for y. Examples are provided finding the intercepts of equations by setting variables equal to 0 and solving.
Topic 4 solving quadratic equations part 1
This document provides instruction on solving quadratic equations. It begins with an introduction to quadratic equations and examples of their real-world applications. It then presents several examples of solving quadratic equations by factoring and setting each factor equal to 0. Various methods are demonstrated including solving by factoring trinomials and binomials. Finally, students are provided practice problems to solve quadratic equations on their own.
5.4 notes
This document discusses how to find the x-intercept and y-intercept of a linear equation by setting one variable equal to 0 and solving for the other. It provides examples of finding intercepts from equations, graphing lines using intercepts, and identifying intercepts from a graph.
TechMathI - Standard form
The document discusses finding the x-intercept and y-intercept of linear equations by setting either x or y equal to 0 and solving for the other variable. It provides examples of finding the intercepts of equations and graphing the resulting point coordinates. Students are asked to practice finding and graphing intercepts for several equations.
4.3.3 find x intercepts by factoring
This document discusses finding x-intercepts by setting a quadratic equation equal to 0 and solving. It also shows examples of finding the value of x given the area of a rectangle or trapezoid. Finally, it asks how much a rectangular area should be increased if both dimensions are doubled to double the total area. The document provides step-by-step workings to solve these types of word problems algebraically.
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.
5.2 using intercepts
This document provides examples and explanations for finding the x- and y-intercepts of linear equations and using intercepts to graph lines. It defines x- and y-intercepts, shows how to find them by setting x or y equal to 0, and explains that intercepts represent important values on the graph like when distance or time is 0. Examples demonstrate finding intercepts, generating points, and graphing lines based on the intercepts.
5.2 using intercepts
This document provides examples and explanations for finding the x- and y-intercepts of linear equations and using intercepts to graph lines. It defines x- and y-intercepts, shows how to find them by setting variables equal to 0 in the equation, and explains that intercepts represent important values when graphing real-world situations. Examples demonstrate finding intercepts, generating ordered pairs, and graphing lines by plotting the intercept points.
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 shows students how to identify the coefficients a, b, and c. The bulk of the document demonstrates two methods for solving quadratic equations: factoring and using the quadratic formula. It includes examples of each method and practice problems for students to work through. The goal is to teach students how to solve quadratic equations through factoring and using the formula.
Chapter 5 Using Intercepts
This document provides examples and explanations for finding the x-intercept and y-intercept of linear equations and using those intercepts to graph the line. It discusses interpreting the intercepts in real world contexts like time to complete a race or amount of items that can be purchased. Students are given examples of finding intercepts, graphing lines by plotting the intercept points, and word problems involving linear equations.
Chapter 5 Using Intercepts
This document provides examples and explanations for finding the x-intercept and y-intercept of linear equations and using those intercepts to graph the line. It discusses interpreting the intercepts in real world contexts like time to complete a race or amount of items that can be purchased. Students are given examples of finding intercepts, graphing lines by plotting the intercept points, and word problems involving linear equations.
2.3 linear equations
The document discusses linear equations and how to graph them. It defines linear equations as having variables with exponents of 1 that are added or subtracted. It explains how to identify the slope and y-intercept of a linear equation in slope-intercept form (y=mx+b) in order to graph it as a line on the coordinate plane. Key steps include solving for y and identifying the slope (m) and y-intercept (b). Examples are provided to demonstrate finding intercepts and graphing various linear equations.
X and y intercept
This document discusses using x-intercepts and y-intercepts to graph linear functions. It provides 4 examples of finding the x-intercept and y-intercept of linear equations by setting either x or y equal to 0 and solving for the other variable. The x-intercept is the x-coordinate where the line crosses the x-axis (when y=0) and the y-intercept is the y-coordinate where the line crosses the y-axis (when x=0).
Ml lesson 4 4
The document discusses finding the x-intercepts and y-intercepts of linear equations. It provides examples of finding the intercepts of equations such as 4x + 2y = 6 and 2x - 3y = 8 by setting either x or y equal to 0. The intercepts are then used to graph the lines on a coordinate plane.
Answers for 4th period exam (review)
Here are the steps to solve this probability problem:
1) Identify the sample space (all possible outcomes): When rolling a standard 6-sided die, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.
2) Identify the favorable outcomes (outcomes we want): The outcomes that result in a number greater than 2 are: 3, 4, 5, 6. There are 4 of these.
3) Calculate the probability:
Probability = Favorable Outcomes / Total Possible Outcomes
= 4 / 6
= 4/6
So the probability of rolling a number greater than 2 on a standard 6-sided die is 4/6.
Lesson 3 finding x and y intercepts shared
The document discusses finding the x-intercepts and y-intercepts of graphs and equations. It defines intercepts as the points where the line crosses the x-axis or y-axis. It then provides examples of finding the intercepts by setting y=0 to find the x-intercept or setting x=0 to find the y-intercept and solving the resulting equation. The document demonstrates this process for multiple equations and graphs. It also introduces the "cover up method" of solving multi-variable equations by covering terms with the same variable to isolate that variable.
Wordproblem
1. The three consecutive integers are 5, 6, 7. The product of the first and last (5 * 7) is one less than five times the middle (5 * 6).
2006_2_2 (2).ppt
This document defines and provides examples of linear equations. It explains that a linear equation has variables with exponents of 1 that are added or subtracted. The document shows examples of linear equations in standard Ax + By = C form and identifies the slope and y-intercept. It also provides examples of nonlinear equations that do not follow the standard linear form. The document describes how to find the x-intercept and y-intercept of a linear equation by setting one variable to 0 and solving for the other. Graphing linear equations in slope-intercept form is also demonstrated.
Linear Equation in two variables
This document defines and provides examples of linear equations. It explains that a linear equation has variables with exponents of 1 that are added or subtracted. The document shows examples of linear equations in standard Ax + By = C form and identifies the slope and y-intercept. It also provides examples of nonlinear equations that do not follow the standard linear form. The document describes how to find the x-intercept and y-intercept of a linear equation by setting one variable equal to 0 and solving for the other. Graphing linear equations in slope-intercept form is also summarized.
Linear equations 2-2 a graphing and x-y intercepts
The document provides information about graphing points and linear equations on the Cartesian coordinate plane. It defines key terms like ordered pairs, x- and y-intercepts, and quadrants. It explains how to graph linear equations by finding x- and y-intercepts or substituting values into the equation to find points. Horizontal and vertical lines are identified, with their equations using either a constant x or y value.
Similar to Lesson graphing using intercepts (20)
Module 10 Topic 4 solving quadratic equations part 1
Module 10 Topic 4 solving quadratic equations part 1
Linear equations 2-2 a graphing and x-y intercepts
Linear equations 2-2 a graphing and x-y intercepts
Recently uploaded
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。
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.
Presentation of the OECD Artificial Intelligence Review of Germany
Consult the full report at https://www.oecd.org/digital/oecd-artificial-intelligence-review-of-germany-609808d6-en.htm
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications.
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 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.
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Microsoft - Power Platform_G.Aspiotis.pdf
Revolutionizing Application Development
with AI-powered low-code, presentation by George Aspiotis, Sr. Partner Development Manager, Microsoft
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.
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.
20 Comprehensive Checklist of Designing and Developing a Website
Dive into the world of Website Designing and Developing with Pixlogix! Looking to create a stunning online presence? Look no further! Our comprehensive checklist covers everything you need to know to craft a website that stands out. From user-friendly design to seamless functionality, we've got you covered. Don't miss out on this invaluable resource! Check out our checklist now at Pixlogix and start your journey towards a captivating online presence today.
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.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
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.
National Security Agency - NSA mobile device best practices
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
Recently uploaded (20)
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...
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Full-RAG: A modern architecture for hyper-personalization
Full-RAG: A modern architecture for hyper-personalization
20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
National Security Agency - NSA mobile device best practices
National Security Agency - NSA mobile device best practices
Lesson graphing using intercepts
- 1. Lesson: Graphing Using Intercepts Courtesy of BSN
- 2. x-intercept – x-coordinate of a point where the graph crosses the x- axis. y-intercept – y-coordinate of a point where the graph crosses the y- axis. y-intercept (0, 2) x-intercept (4, 0)
- 3. EX Find the x-intercept and the y-intercept of the graph of 2x + 3y = 12. y-intercept x-intercept Let x = 0. Let y = 0. 2 x 3 y 12 2 x 3 y 12 2(0) 3 y 12 2x 3(0) 12 3y 12 2x 12 3 3 2 2 y 4 x 6 (0, 4) (6, 0)
- 4. EX Graph the equation 3x + 5y = 15 using intercepts. y-intercept x-intercept Let x = 0. Let y = 0. 3x 5 y 15 3x 5 y 15 3(0) 5 y 15 3x 5(0) 15 5y 15 3x 15 5 5 3 3 y 3 x 5 • •
- 5. EX You are helping to plan a dinner at your school and you need to rent tables to seat 144 people. Small tables seat 6 people and large tables seat 8 people. 6x + 8y = 144 x = number of small tables y = number of large tables a. Find the intercepts and graph the equation. b. Give four possibilities for the numbers of each size table. y-intercept x-intercept Let x = 0. Let y = 0. 6 x 8 y 144 6 x 8 y 144 6(0) 8 y 144 6x 8(0) 144 8y 144 6x 144 8 8 6 6 y 18 x 24 • 0 small and 18 large 24 small and 0 large • 8 small and 12 large 16 small and 6 large