## Ninth grade Lesson Introduction to Quadratic Functions

Characteristics of Quadratics Worksheet. Name: _____ Types of Functions Worksheet Algebra 1 For #1-15, state whether or not each graph shows a function. If it is a function, say whether it is linear, quadratic, absolute value, exponential, or none of the above. 1. 2. 3. Function? Yes or No Function? Yes or No Function? Yes or No, Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line.

### 1 EXPLORATION Identifying Graphs of Quadratic Functions

QUADRATIC FUNCTIONS KEY FEATURES Identifying Key Features. If a quadratic function has a vertex at (5, 3) and x-intercepts at 4 and 6, what does the y-value of the vertex represent? Explain. 40. If a quadratic function has a vertex at ( 1, 8) and x-intercepts at 3 and 1, what does the y-value of the vertex represent? Explain. 41. The axis of symmetry of a parabola is x 2 3., quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9.

Quadratic Functions 1. I can identify a function as quadratic given a table, equation, or graph. 2. I can determine the appropriate domain and range of a quadratic equation or event. 3. I can identify the minimum or maximum and zeros of a function with a calculator. 4. I can apply quadratic functions to model real-life situations, including quadratic regression models from data. Graphing 5. I Identifying Exponential Functions from a Table В A function is said to be an exponential function if equal steps in the independent variable produce equal ratios for the dependent variable. В Ex. Does the following table represent an exponential function?

WORKSHEET 9-5 Algebra 1 Name _____ Class Hour _____ Directions: Short Answer 1. Does the discriminant give the exact roots of a quadratic equation (The points where the parabola crosses the x-axis)? 2. How is the discriminant related to the quadratic formula? 3. Explain WHYвЂ¦ a. Which of the relations are functions? Try to spot functions from ordered pairs, mapping diagrams, input-output tables, graphs and equations with this unit of pdf worksheets. Function Table Worksheets. These printable function table worksheets provide practice with different types of functions like linear, quadratic, polynomial, and more. Plug an input value in the function rule and write the output.

Practice A Identifying Quadratic Functions Tell whether each function is quadratic. Explain. 1. x 12 3 4 5 y 03 8 15 24 2. y 5 2 x 2 yes yes the second differences are constant. it can be written in the form y ax 2 bx c. 3. Use the table of values to graph y x 2 4. xy x 2 4 x, вЂ¦ 2. Brief description of the lesson: To help students understand the relevance of quadratic functions to real life and the importance of the critical points of a quadratic graph. 3. Aims of the Lesson: ShortвЂђterm aims IвЂ™d like my students to recognise quadratic functions. IвЂ™d like my students to recognise the graph of a quadratic function.

I. Quadratic Functions A. The basics The graph of a quadratic function is a parabola. A parabola for a quadratic function can open up or down, but not left or right. The vertex is either the highest or lowest point on the graph depending on whether it opens up or down. If the parabola opens down, the vertex is the highest point. y x Vertex/Minimum Vertex/ Maximum Axis of Symmetry Parabolas 2. Brief description of the lesson: To help students understand the relevance of quadratic functions to real life and the importance of the critical points of a quadratic graph. 3. Aims of the Lesson: ShortвЂђterm aims IвЂ™d like my students to recognise quadratic functions. IвЂ™d like my students to recognise the graph of a quadratic function.

Quadratic functions from the real world have been sought through the internet. Quadratic functions in real-life contexts have been created using GeoGebra. About the Unit and the Lesson This lesson aims to give students an understanding of how the roots of a function on a graph can be used to formulate that function. It is hoped that students will be able to find ways of completing this Identifying Parts of a Quadratic Function Worksheet Great complement to an introductory lesson on Quadratic Functions. Given the quadratic equation, students will create a Table of Values, identify the Axis of Symmetry, Vertex (maximum or minimum), X-Intercept/s, Y-Intercepts, and its Solutions/Zeros/Roots.

WORKSHEET 9-5 Algebra 1 Name _____ Class Hour _____ Directions: Short Answer 1. Does the discriminant give the exact roots of a quadratic equation (The points where the parabola crosses the x-axis)? 2. How is the discriminant related to the quadratic formula? 3. Explain WHYвЂ¦ a. If a quadratic function has a vertex at (5, 3) and x-intercepts at 4 and 6, what does the y-value of the vertex represent? Explain. 40. If a quadratic function has a vertex at ( 1, 8) and x-intercepts at 3 and 1, what does the y-value of the vertex represent? Explain. 41. The axis of symmetry of a parabola is x 2 3.

Practice: Identify the Vertex, Minimum/Maximum (state which one and what it is), Axis of Symmetry, Domain, Range, and the Zeros/Roots/Solutions of each quadratic function graphed below. O В©U U2b0 D1S2Z PKPu6t RaT bS To AfSt1w La Rrce E 2LWLICs. c m WAKlWlP Yrnilg ahhtls4 LrSe2sTe5rDv6eRdx.o T NMua cdKeM OwBiEt yhW 7IonBf ziCnAiLtZeD nA yl ig Ueeb wr1aN e2 H.h Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Vertex Form of Parabolas Date_____ Period____

В©U U2b0 D1S2Z PKPu6t RaT bS To AfSt1w La Rrce E 2LWLICs. c m WAKlWlP Yrnilg ahhtls4 LrSe2sTe5rDv6eRdx.o T NMua cdKeM OwBiEt yhW 7IonBf ziCnAiLtZeD nA yl ig Ueeb wr1aN e2 H.h Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Vertex Form of Parabolas Date_____ Period____ WORKSHEET: Using Transformations to Graph Quadratic Functions Describe the (x + 2) 2 + 3 8. y = - 2 1 (x вЂ“ 1) 2 + 3 9. y = (x + 3) 2 10. y = -(x вЂ“ 1) 2 + 4 Write the equation for the function y = x2 with the following transformations. 11. reflect across the x-axis, shift down 1 12. vertically stretch by a factor of 3, shift right 5 and up 1 13. shift up 5 14. reflect across the x-axis

### Introduction to Quadratic Functions Notes Key

Graphs of quadratic functions and using graphs to solve. Quadratic Functions A quadratic function is an equation in the form y = ax2 + bx + c, where a, b, and c are real numbers and a 0. The shape of a quadratic function is a _____, a smooth and symmetric U-shape. Example 4: Use the table of values below to graph the quadratic function. x y -1 -1 0 -4 1 -5 2 -4 3 -1, quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that a solution exists, analogous to the.

Quadratic Equation Worksheets with Answer Keys. Free pdfs. Characteristics of Quadratic Functions Fill in the blanks and the y column of the chart. Complete the following. 1. Identify the values of a, b, and c in the quadratic function y = 3 x2 в€’ 5 x + 2. _____ 2. Does the graph of the function y = 3 x2 в€’ 5 x + 2 open upward or downward?, If a quadratic function has a vertex at (5, 3) and x-intercepts at 4 and 6, what does the y-value of the vertex represent? Explain. 40. If a quadratic function has a vertex at ( 1, 8) and x-intercepts at 3 and 1, what does the y-value of the vertex represent? Explain. 41. The axis of symmetry of a parabola is x 2 3..

### Name Types of Functions Worksheet For #1-15 state

Characteristics of Quadratic Functions Practice Worksheet. 10.) Write the vertex form of a quadratic equation. 11.) What does changing the вЂњaвЂќ variable do to the graph of a quadratic? 12.) If вЂњhвЂќ is positive how does the parabola move? Negative? 13.) What does changing the вЂњkвЂќ variable do to the graph of a quadratic? 14.) What conclusion can you make about the variables h and k together? https://en.m.wikipedia.org/wiki/Equation 2.1 Transformations of Quadratic Functions For use with Exploration 2.1 Name _____ Date _____ Essential Question How do the constants a, h, and k affect the graph of the quadratic function gx ax h k() ( )=в€’+2? Work with a partner. Match each quadratic function with its graph. Explain your.

For #7-8, a quadratic function and its graph are shown. Identify the solutions, or roots, of the Identify the solutions, or roots, of the related quadratic equation. Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER The table of values represents a quadratic function. x вЂ“2 вЂ“1 0 1 2 y вЂ“6 вЂ“6 вЂ“4 0 6 First differences: 0 2 4 6

Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior. 10.) Write the vertex form of a quadratic equation. 11.) What does changing the вЂњaвЂќ variable do to the graph of a quadratic? 12.) If вЂњhвЂќ is positive how does the parabola move? Negative? 13.) What does changing the вЂњkвЂќ variable do to the graph of a quadratic? 14.) What conclusion can you make about the variables h and k together?

Identifying Parts of a Quadratic Function Worksheet Great complement to an introductory lesson on Quadratic Functions. Given the quadratic equation, students will create a Table of Values, identify the Axis of Symmetry, Vertex (maximum or minimum), X-Intercept/s, Y-Intercepts, and its Solutions/Zeros/Roots. 7) 8) 9) Printable Math Worksheets @ www.mathworksheets4kids.com Answer key 1) 2) 3)-5 -4 -3 -2 -1 1 2 3 4 5 5 4 3 2 1-1-2-3-4-5 4) 5) 6) zeros : = В±20 and = В±8

Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line WORKSHEET: Using Transformations to Graph Quadratic Functions Describe the (x + 2) 2 + 3 8. y = - 2 1 (x вЂ“ 1) 2 + 3 9. y = (x + 3) 2 10. y = -(x вЂ“ 1) 2 + 4 Write the equation for the function y = x2 with the following transformations. 11. reflect across the x-axis, shift down 1 12. vertically stretch by a factor of 3, shift right 5 and up 1 13. shift up 5 14. reflect across the x-axis

The shape of a quadratic equation is called a _____ 5. When the vertex is the highest point on the graph, we call that a _____. 6. When the vertex is the lowest point on the graph, we call that a _____. 7. Our solutions are the _____. 8. Solutions to quadratic equations are called _____. 608 Chapter 9 Previously, you вЂ identified and graphed linear functions. вЂ transformed linear functions. вЂ solved linear equations. вЂ factored quadratic polynomials, including perfect-square trinomials. You will study вЂ identifying and graphing quadratic functions. вЂ transforming quadratic equations. вЂ solving quadratic equations. вЂ using factoring to graph

Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER The table of values represents a quadratic function. x вЂ“2 вЂ“1 0 1 2 y вЂ“6 вЂ“6 вЂ“4 0 6 First differences: 0 2 4 6 2.1 Transformations of Quadratic Functions For use with Exploration 2.1 Name _____ Date _____ Essential Question How do the constants a, h, and k affect the graph of the quadratic function gx ax h k() ( )=в€’+2? Work with a partner. Match each quadratic function with its graph. Explain your

Work through the quiz and worksheet to see what you know about identifying quadratics. The questions on the quiz let you gain practice in this area... quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9

quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9 Name: _____ Types of Functions Worksheet Algebra 1 For #1-15, state whether or not each graph shows a function. If it is a function, say whether it is linear, quadratic, absolute value, exponential, or none of the above. 1. 2. 3. Function? Yes or No Function? Yes or No Function? Yes or No

## Name Class Date PreAssessment Quadratic Unit

Ninth grade Lesson Introduction to Quadratic Functions. Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line, Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior..

### Introducing quadratic functions through problem solving

Identifying the Parts of Quadratic Functions Worksheet. Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior., 608 Chapter 9 Previously, you вЂ identified and graphed linear functions. вЂ transformed linear functions. вЂ solved linear equations. вЂ factored quadratic polynomials, including perfect-square trinomials. You will study вЂ identifying and graphing quadratic functions. вЂ transforming quadratic equations. вЂ solving quadratic equations. вЂ using factoring to graph.

Ixl identify linear quadratic and exponential functions from tables algebra 1 practice how to tell if a table is linear quadratic or exponential this is a quadratic model because the second differences are that have same value 4 note when you compare difference of 10 7 linear exponential and quadratic... Work through the quiz and worksheet to see what you know about identifying quadratics. The questions on the quiz let you gain practice in this area...

Name: _____ Types of Functions Worksheet Algebra 1 For #1-15, state whether or not each graph shows a function. If it is a function, say whether it is linear, quadratic, absolute value, exponential, or none of the above. 1. 2. 3. Function? Yes or No Function? Yes or No Function? Yes or No Which of the relations are functions? Try to spot functions from ordered pairs, mapping diagrams, input-output tables, graphs and equations with this unit of pdf worksheets. Function Table Worksheets. These printable function table worksheets provide practice with different types of functions like linear, quadratic, polynomial, and more. Plug an input value in the function rule and write the output.

2.1 Transformations of Quadratic Functions For use with Exploration 2.1 Name _____ Date _____ Essential Question How do the constants a, h, and k affect the graph of the quadratic function gx ax h k() ( )=в€’+2? Work with a partner. Match each quadratic function with its graph. Explain your Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay.

Page 1 of 2 5.1 Graphing Quadratic Functions 249 Graphing Quadratic Functions GRAPHING A QUADRATIC FUNCTION A has the form y = ax2 + bx + c where a в‰ 0. The graph of a quadratic function is U-shaped and is called a For instance, the graphs of y = x2 and y = Вєx2 are shown at the right. Quadratic Sequences Quadratic sequences take the form рќ’Џ + рќ’Џ+ For each of the following quadratic sequences, identify the values of a, b and c:

Graphs of Quadratic Functions Worksheet 1к…‡Features of Quadratic Graphs (1) Questions: 1. Press Гђ or ГЏ button to set the values of a, b and c to 1, 0 and 0 respectively. The figure above shows the graph of y = _____. 2. Keep the values of b and c to 0.Press ГЏ button to increase the value of a gradually from 1 to 4. Page 1 of 2 5.1 Graphing Quadratic Functions 249 Graphing Quadratic Functions GRAPHING A QUADRATIC FUNCTION A has the form y = ax2 + bx + c where a в‰ 0. The graph of a quadratic function is U-shaped and is called a For instance, the graphs of y = x2 and y = Вєx2 are shown at the right.

6. Match the quadratic function fx to its characteristics: 1. The interval of increase is f ,2 . 2. The range is d f8 f x . 3. The axis of symmetry is located at x = 8. 4. The interval of decrease is f x8. A. B. C. D. quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9

If a quadratic function has a vertex at (5, 3) and x-intercepts at 4 and 6, what does the y-value of the vertex represent? Explain. 40. If a quadratic function has a vertex at ( 1, 8) and x-intercepts at 3 and 1, what does the y-value of the vertex represent? Explain. 41. The axis of symmetry of a parabola is x 2 3. 10.) Write the vertex form of a quadratic equation. 11.) What does changing the вЂњaвЂќ variable do to the graph of a quadratic? 12.) If вЂњhвЂќ is positive how does the parabola move? Negative? 13.) What does changing the вЂњkвЂќ variable do to the graph of a quadratic? 14.) What conclusion can you make about the variables h and k together?

The shape of a quadratic equation is called a _____ 5. When the vertex is the highest point on the graph, we call that a _____. 6. When the vertex is the lowest point on the graph, we call that a _____. 7. Our solutions are the _____. 8. Solutions to quadratic equations are called _____. Quadratic Functions 1. I can identify a function as quadratic given a table, equation, or graph. 2. I can determine the appropriate domain and range of a quadratic equation or event. 3. I can identify the minimum or maximum and zeros of a function with a calculator. 4. I can apply quadratic functions to model real-life situations, including quadratic regression models from data. Graphing 5. I

### Name Types of Functions Worksheet For #1-15 state

Identifying Zeros Sheet 1 Math Worksheets 4 Kids. For #7-8, a quadratic function and its graph are shown. Identify the solutions, or roots, of the Identify the solutions, or roots, of the related quadratic equation., Quadratic Sequences Quadratic sequences take the form рќ’Џ + рќ’Џ+ For each of the following quadratic sequences, identify the values of a, b and c:.

### Properties of Quadratic Functions collegeprepalgebra.com

05 Quadratic Formula. Prac+ice! + Axis of Symmetry: a-ox O V rtex: Domain: Range: bx+c S+eps qncp-Q4fc eqJ0Jm Step 1: Step 2: step 3: Step 4: Find the axis of symmetry, https://en.m.wikipedia.org/wiki/Equation Page 8 ____ 20 A rocket is launched from atop a 56-foot cliff with an initial velocity of 135 ft/s. Substitute the values into the vertical motion formula h= в€’16t 2 +vt+c. Let h = 0. Use the quadratic formula find out how long the rocket will take to hit the ground after it is.

Graphs of Quadratic Functions Worksheet 1к…‡Features of Quadratic Graphs (1) Questions: 1. Press Гђ or ГЏ button to set the values of a, b and c to 1, 0 and 0 respectively. The figure above shows the graph of y = _____. 2. Keep the values of b and c to 0.Press ГЏ button to increase the value of a gradually from 1 to 4. Name_____ Date _____ Class _____ Quadratic Functions вЂ“ Identifying Key Features of Quadratic Graphs В© Math Square by Pierceson Le Identify key features of

Graphs of Quadratic Functions Worksheet 1к…‡Features of Quadratic Graphs (1) Questions: 1. Press Гђ or ГЏ button to set the values of a, b and c to 1, 0 and 0 respectively. The figure above shows the graph of y = _____. 2. Keep the values of b and c to 0.Press ГЏ button to increase the value of a gradually from 1 to 4. quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9

Quadratic functions from the real world have been sought through the internet. Quadratic functions in real-life contexts have been created using GeoGebra. About the Unit and the Lesson This lesson aims to give students an understanding of how the roots of a function on a graph can be used to formulate that function. It is hoped that students will be able to find ways of completing this Page 8 ____ 20 A rocket is launched from atop a 56-foot cliff with an initial velocity of 135 ft/s. Substitute the values into the vertical motion formula h= в€’16t 2 +vt+c. Let h = 0. Use the quadratic formula find out how long the rocket will take to hit the ground after it is

Quadratic Functions Quiz Score: ____ out of 42 Part One: Multiple Choice (2 points each.) Identify the choice that best completes the statement or answers the question. ____ 1. Tell whether the graph of the quadratic function opens upward or downward. Explain. 1) Because , the parabola opens downward. 2) Because , the parabola opens downward. 608 Chapter 9 Previously, you вЂ identified and graphed linear functions. вЂ transformed linear functions. вЂ solved linear equations. вЂ factored quadratic polynomials, including perfect-square trinomials. You will study вЂ identifying and graphing quadratic functions. вЂ transforming quadratic equations. вЂ solving quadratic equations. вЂ using factoring to graph

quadratic function. ! y = 2x2 вЂ“ x + 6 ! The x-values are consistently increasing by one, the first differences are not the same, there this relation is not linear, the second difference are equal, therefore this relation represents a quadratic function. x y 1st 2nd -3 27 -11 4 -2 16 -9 4 -1 9 -3 4 0 6 1 4 1 7 5 4 2 12 9 WORKSHEET 9-5 Algebra 1 Name _____ Class Hour _____ Directions: Short Answer 1. Does the discriminant give the exact roots of a quadratic equation (The points where the parabola crosses the x-axis)? 2. How is the discriminant related to the quadratic formula? 3. Explain WHYвЂ¦ a.

quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that a solution exists, analogous to the Characteristics of Quadratic Functions Fill in the blanks and the y column of the chart. Complete the following. 1. Identify the values of a, b, and c in the quadratic function y = 3 x2 в€’ 5 x + 2. _____ 2. Does the graph of the function y = 3 x2 в€’ 5 x + 2 open upward or downward?

Practice A Identifying Quadratic Functions Tell whether each function is quadratic. Explain. 1. x 12 3 4 5 y 03 8 15 24 2. y 5 2 x 2 yes yes the second differences are constant. it can be written in the form y ax 2 bx c. 3. Use the table of values to graph y x 2 4. xy x 2 4 x, вЂ¦ The shape of a quadratic equation is called a _____ 5. When the vertex is the highest point on the graph, we call that a _____. 6. When the vertex is the lowest point on the graph, we call that a _____. 7. Our solutions are the _____. 8. Solutions to quadratic equations are called _____.

## Function Worksheets

WORKSHEET Using Transformations to Graph Quadratic Functions. В©G 62 T0N1X2r ZK Iu kt jaM oSio gfWt7w Fa LrIe e HLhLyC J.1 O bA Vl8lh RrQirg uhgtWsP 2r 1eEssevr yvAePdg.o x TMIaOdReh dwji gt Jhe 2I dnwffi Mnniot ze2 TA6lzgUe0bTroa m O2W.r Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Properties of Parabolas Date_____ Period____, В©G 62 T0N1X2r ZK Iu kt jaM oSio gfWt7w Fa LrIe e HLhLyC J.1 O bA Vl8lh RrQirg uhgtWsP 2r 1eEssevr yvAePdg.o x TMIaOdReh dwji gt Jhe 2I dnwffi Mnniot ze2 TA6lzgUe0bTroa m O2W.r Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Properties of Parabolas Date_____ Period____.

### Properties of Quadratic Functions collegeprepalgebra.com

Function Worksheets. I. Quadratic Functions A. The basics The graph of a quadratic function is a parabola. A parabola for a quadratic function can open up or down, but not left or right. The vertex is either the highest or lowest point on the graph depending on whether it opens up or down. If the parabola opens down, the vertex is the highest point. y x Vertex/Minimum Vertex/ Maximum Axis of Symmetry Parabolas, Section 2.1 Transformations of Quadratic Functions 51 Writing a Transformed Quadratic Function Let the graph of g be a translation 3 units right and 2 units up, followed by a refl ection in the y-axis of the graph of f(x) = x2 в€’ 5x.Write a rule for g. SOLUTION Step 1 First write a function h that represents the translation of f. h(x) = f(x в€’ 3) + 2 Subtract 3 from the input..

Quadratic Functions A quadratic function is an equation in the form y = ax2 + bx + c, where a, b, and c are real numbers and a 0. The shape of a quadratic function is a _____, a smooth and symmetric U-shape. Example 4: Use the table of values below to graph the quadratic function. x y -1 -1 0 -4 1 -5 2 -4 3 -1 Graphs of Quadratic Functions Worksheet 1к…‡Features of Quadratic Graphs (1) Questions: 1. Press Гђ or ГЏ button to set the values of a, b and c to 1, 0 and 0 respectively. The figure above shows the graph of y = _____. 2. Keep the values of b and c to 0.Press ГЏ button to increase the value of a gradually from 1 to 4.

Quadratic functions from the real world have been sought through the internet. Quadratic functions in real-life contexts have been created using GeoGebra. About the Unit and the Lesson This lesson aims to give students an understanding of how the roots of a function on a graph can be used to formulate that function. It is hoped that students will be able to find ways of completing this Characteristics of Quadratic Functions Fill in the blanks and the y column of the chart. Complete the following. 1. Identify the values of a, b, and c in the quadratic function y = 3 x2 в€’ 5 x + 2. _____ 2. Does the graph of the function y = 3 x2 в€’ 5 x + 2 open upward or downward?

I. Quadratic Functions A. The basics The graph of a quadratic function is a parabola. A parabola for a quadratic function can open up or down, but not left or right. The vertex is either the highest or lowest point on the graph depending on whether it opens up or down. If the parabola opens down, the vertex is the highest point. y x Vertex/Minimum Vertex/ Maximum Axis of Symmetry Parabolas Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior.

Prac+ice! + Axis of Symmetry: a-ox O V rtex: Domain: Range: bx+c S+eps qncp-Q4fc eqJ0Jm Step 1: Step 2: step 3: Step 4: Find the axis of symmetry, Quadratic Functions A quadratic function is an equation in the form y = ax2 + bx + c, where a, b, and c are real numbers and a 0. The shape of a quadratic function is a _____, a smooth and symmetric U-shape. Example 4: Use the table of values below to graph the quadratic function. x y -1 -1 0 -4 1 -5 2 -4 3 -1

Section 2.1 Transformations of Quadratic Functions 51 Writing a Transformed Quadratic Function Let the graph of g be a translation 3 units right and 2 units up, followed by a refl ection in the y-axis of the graph of f(x) = x2 в€’ 5x.Write a rule for g. SOLUTION Step 1 First write a function h that represents the translation of f. h(x) = f(x в€’ 3) + 2 Subtract 3 from the input. Worksheet by Kuta Software LLC-4-13) 3r2 - 12r = 1514) 2n2 - 12 = 5n For each function, a) determine if it opens up or down, b) find the axis of symmetry, c) find the vertex, d) find the y - intercept, e) graph the function, f) determine if it has a maximum or minimum and what that value is, and g) identify the domain and range. 15) f (x

Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line

10.) Write the vertex form of a quadratic equation. 11.) What does changing the вЂњaвЂќ variable do to the graph of a quadratic? 12.) If вЂњhвЂќ is positive how does the parabola move? Negative? 13.) What does changing the вЂњkвЂќ variable do to the graph of a quadratic? 14.) What conclusion can you make about the variables h and k together? For #7-8, a quadratic function and its graph are shown. Identify the solutions, or roots, of the Identify the solutions, or roots, of the related quadratic equation.

### Identify Non-linear Functions from Data Math Interventions

Vertex Form of Parabolas Kuta Software LLC. 6. Match the quadratic function fx to its characteristics: 1. The interval of increase is f ,2 . 2. The range is d f8 f x . 3. The axis of symmetry is located at x = 8. 4. The interval of decrease is f x8. A. B. C. D., Quadratic functions from the real world have been sought through the internet. Quadratic functions in real-life contexts have been created using GeoGebra. About the Unit and the Lesson This lesson aims to give students an understanding of how the roots of a function on a graph can be used to formulate that function. It is hoped that students will be able to find ways of completing this.

Name Types of Functions Worksheet For #1-15 state. Practice A Identifying Quadratic Functions Tell whether each function is quadratic. Explain. 1. x 12 3 4 5 y 03 8 15 24 2. y 5 2 x 2 yes yes the second differences are constant. it can be written in the form y ax 2 bx c. 3. Use the table of values to graph y x 2 4. xy x 2 4 x, вЂ¦, Name: _____ Types of Functions Worksheet Algebra 1 For #1-15, state whether or not each graph shows a function. If it is a function, say whether it is linear, quadratic, absolute value, exponential, or none of the above. 1. 2. 3. Function? Yes or No Function? Yes or No Function? Yes or No.

### Quadratic Relations Weebly

Properties of Parabolas Kuta Software LLC. Quadratic Sequences Quadratic sequences take the form рќ’Џ + рќ’Џ+ For each of the following quadratic sequences, identify the values of a, b and c: https://en.m.wikipedia.org/wiki/Equation Quadratic Sequences Quadratic sequences take the form рќ’Џ + рќ’Џ+ For each of the following quadratic sequences, identify the values of a, b and c:.

Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line I have students complete the 3 examples for the Quadratic Functions given in Vertex Form, Standard Form, and Intercept form. I also have students write down the notes with each one. I do not explain the different forms at this time. I want students to complete the foldable to refer back to in the next activity, and to use later in this unit.

I. Quadratic Functions A. The basics The graph of a quadratic function is a parabola. A parabola for a quadratic function can open up or down, but not left or right. The vertex is either the highest or lowest point on the graph depending on whether it opens up or down. If the parabola opens down, the vertex is the highest point. y x Vertex/Minimum Vertex/ Maximum Axis of Symmetry Parabolas 2.1 Transformations of Quadratic Functions For use with Exploration 2.1 Name _____ Date _____ Essential Question How do the constants a, h, and k affect the graph of the quadratic function gx ax h k() ( )=в€’+2? Work with a partner. Match each quadratic function with its graph. Explain your

WORKSHEET 9-5 Algebra 1 Name _____ Class Hour _____ Directions: Short Answer 1. Does the discriminant give the exact roots of a quadratic equation (The points where the parabola crosses the x-axis)? 2. How is the discriminant related to the quadratic formula? 3. Explain WHYвЂ¦ a. Identifying Parts of a Quadratic Function Worksheet Great complement to an introductory lesson on Quadratic Functions. Given the quadratic equation, students will create a Table of Values, identify the Axis of Symmetry, Vertex (maximum or minimum), X-Intercept/s, Y-Intercepts, and its Solutions/Zeros/Roots.

В©U U2b0 D1S2Z PKPu6t RaT bS To AfSt1w La Rrce E 2LWLICs. c m WAKlWlP Yrnilg ahhtls4 LrSe2sTe5rDv6eRdx.o T NMua cdKeM OwBiEt yhW 7IonBf ziCnAiLtZeD nA yl ig Ueeb wr1aN e2 H.h Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Vertex Form of Parabolas Date_____ Period____ For #7-8, a quadratic function and its graph are shown. Identify the solutions, or roots, of the Identify the solutions, or roots, of the related quadratic equation.

Quadratic Functions 1. I can identify a function as quadratic given a table, equation, or graph. 2. I can determine the appropriate domain and range of a quadratic equation or event. 3. I can identify the minimum or maximum and zeros of a function with a calculator. 4. I can apply quadratic functions to model real-life situations, including quadratic regression models from data. Graphing 5. I Prac+ice! + Axis of Symmetry: a-ox O V rtex: Domain: Range: bx+c S+eps qncp-Q4fc eqJ0Jm Step 1: Step 2: step 3: Step 4: Find the axis of symmetry,

Practice: Identify the Vertex, Minimum/Maximum (state which one and what it is), Axis of Symmetry, Domain, Range, and the Zeros/Roots/Solutions of each quadratic function graphed below. O Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER The table of values represents a quadratic function. x вЂ“2 вЂ“1 0 1 2 y вЂ“6 вЂ“6 вЂ“4 0 6 First differences: 0 2 4 6

Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER The table of values represents a quadratic function. x вЂ“2 вЂ“1 0 1 2 y вЂ“6 вЂ“6 вЂ“4 0 6 First differences: 0 2 4 6 quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that a solution exists, analogous to the

Quadratic Sequences Quadratic sequences take the form рќ’Џ + рќ’Џ+ For each of the following quadratic sequences, identify the values of a, b and c: Quadratic Functions Quiz Score: ____ out of 42 Part One: Multiple Choice (2 points each.) Identify the choice that best completes the statement or answers the question. ____ 1. Tell whether the graph of the quadratic function opens upward or downward. Explain. 1) Because , the parabola opens downward. 2) Because , the parabola opens downward.

Name: _____ Types of Functions Worksheet Algebra 1 For #1-15, state whether or not each graph shows a function. If it is a function, say whether it is linear, quadratic, absolute value, exponential, or none of the above. 1. 2. 3. Function? Yes or No Function? Yes or No Function? Yes or No Prac+ice! + Axis of Symmetry: a-ox O V rtex: Domain: Range: bx+c S+eps qncp-Q4fc eqJ0Jm Step 1: Step 2: step 3: Step 4: Find the axis of symmetry,

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