# Identifying Quadratic Functions Worksheet Pdf

Quiz & Worksheet Identifying Quadratics Study.com. Free worksheet with answer keys on quadratic equations. Each one has model problems worked out step by step, practice problems, challenge proglems, Created by GradeAmathhelp.com, all rights reserved. Determine if the following are functionsвЂ¦ Write вЂњfunctionвЂќ or вЂњnot functionвЂќ on the line.

### LESSON Practice A Identifying Quadratic Functions

Graphing Quadratic Functions. 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., 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¦.

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. Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior.

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. 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?

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 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.

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 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?

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 _____. 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

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? 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.

Analytic Geometry Name: _____ Characteristics of Quadratic Functions Worksheet Find the following Characteristics of each graph. 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 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 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 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 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 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

### 10.8 Compare Linear Exponential and Quadratic Models

Quadratic Relations Weebly. 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., 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 Relations Weebly. 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, 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..

### 2.1 Transformations of Quadratic Functions

Graphing Quadratic Functions Notes Key. Name_____ Date _____ Class _____ Quadratic Functions вЂ“ Identifying Key Features of Quadratic Graphs В© Math Square by Pierceson Le Identify key features of https://en.m.wikipedia.org/wiki/Equation The function is increasing to the left of x = 4 and decreasing to the right of x = 4, as shown in the п¬Ѓ gure. Analyzing a Quadratic Function Properties of Quadratic Functions В®. Analyzing a Quadratic Function In Exercises 1в€’6, describe the domain and range of the function, and determine where the function is increasing or decreasing..

• Name Types of Functions Worksheet For #1-15 state
• Ninth grade Lesson Introduction to Quadratic Functions

• 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 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...

Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay. 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 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. 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

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 6 608 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 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 functions in the form , where y is being defined as the quadratic function . In most high school math classrooms students interact with quadratic functions in which a, b, and c are integers. Teachers and students also work with quadratic equations that result from setting a quadratic expression equal to a 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, 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. Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior.

Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay. 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?

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. 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

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. 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.

## Graphing Quadratic Functions Notes Key

Quadratic Word Problems Mr. Free's Math Domain. Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay., 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 Word Problems Mr. Free's Math Domain

QUADRATIC FUNCTIONS KEY FEATURES Identifying Key Features. 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____, Identifying and Interpreting Key Features of Quadratic Functions Lesson Objective Students will identify the key features of a quadratic function, including intercepts, maximums and minimums, using a graphing calculator and interpret their meaning in real-world applications..

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. Identifying and Interpreting Key Features of Quadratic Functions Lesson Objective Students will identify the key features of a quadratic function, including intercepts, maximums and minimums, using a graphing calculator and interpret their meaning in real-world applications.

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____ 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

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. 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.

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. 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 _____.

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? Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay.

Free worksheet with answer keys on quadratic equations. Each one has model problems worked out step by step, practice problems, challenge proglems 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 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 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...

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. Name_____ Date _____ Class _____ Quadratic Functions вЂ“ Identifying Key Features of Quadratic Graphs В© Math Square by Pierceson Le Identify key features of

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 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

Free worksheet with answer keys on quadratic equations. Each one has model problems worked out step by step, practice problems, challenge proglems 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?

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 Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior.

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 Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay.

Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior. 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

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 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: 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 Name_____ Date _____ Class _____ Quadratic Functions вЂ“ Identifying Key Features of Quadratic Graphs В© Math Square by Pierceson Le Identify key features of

Comparing Linear, Quadratic, and Exponential Worksheet Identify the following as Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential Decay. 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.

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... Analytic Geometry Name: _____ Characteristics of Quadratic Functions Worksheet Find the following Characteristics of each graph.

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? 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

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 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.

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____ Identifying and Interpreting Key Features of Quadratic Functions Lesson Objective Students will identify the key features of a quadratic function, including intercepts, maximums and minimums, using a graphing calculator and interpret their meaning in real-world applications.

Introducing quadratic functions through problem solving. 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., 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..

### Algebra 2 and Trigonometry Chapter 4 FUNCTIONS

Graphing Quadratic Functions. 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?, Identify NonвЂђlinear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior..

### Characteristics of Quadratic Functions

1 EXPLORATION Identifying Graphs of Quadratic Functions. 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. 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:.

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. 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¦

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

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. 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 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 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____

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 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

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 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.

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? The function is increasing to the left of x = 4 and decreasing to the right of x = 4, as shown in the п¬Ѓ gure. Analyzing a Quadratic Function Properties of Quadratic Functions В®. Analyzing a Quadratic Function In Exercises 1в€’6, describe the domain and range of the function, and determine where the function is increasing or decreasing.

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

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 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:

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? 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____

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

Analytic Geometry Name: _____ Characteristics of Quadratic Functions Worksheet Find the following Characteristics of each graph. 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 _____.

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. 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 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.

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. 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.

Identifying and Interpreting Key Features of Quadratic Functions Lesson Objective Students will identify the key features of a quadratic function, including intercepts, maximums and minimums, using a graphing calculator and interpret their meaning in real-world applications. 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...

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 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

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____ 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,

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? 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.

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. 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 _____.

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. 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.