Algebra 2 Honors Lesson 10 Translating Functions

Size: px
Start display at page:

Download "Algebra 2 Honors Lesson 10 Translating Functions"

Transcription

1 Algebra 2 Honors Lesson 10 Translating Functions Objectives: The students will be able to translate a base function horizontally and vertically. Students will be able to describe the translation of f(x) to g(x), given that g(x) = f(x h) + k. Students will determine that the vertex of f(x) = (x h) 2 + k is (h, k). Materials: Hw #2-9 answers overhead; tally sheets; Translating Functions handouts and overheads; note-taking templates; homework #2-10: translation practice Time Activity 10 min Homework Review Students check their answers to hw #2-9 and discuss work with their group. Pass around a tally sheet for questions (one from each side of the room to speed it up). 5 min Homework Presentations Review the top 2 or 3 questions from the tally sheet. Problems to grade: 20 min Do Now Hand out the Translating Functions worksheet to students. Problem 1 has two parabolas, where the second is a vertical translation of the first. Problem 2 has two parabolas also, where the second is a horizontal translation of the first. Ask students to do these, but to skip the calculator parts for now. 25 min Group Work Show the graphs from parts 1 and 2 on the overhead and take any questions. Now, students should work on the calculator portions of the translations worksheet. 20 min Direct Instruction Lesson Name: Translating Functions Portfolio Section: Functions Background: To translate in math means to move a graph from one place to another. Concepts: Vertical Shift - The graph of y = f(x) + k is the same as the graph of y = f(x), except shifted vertically by k steps. - If k < 0, then f(x) is shifted down. - If k > 0, then f(x) is shifted up. Horizontal Shift - The graph of y = f(x h) is the same as the graph of y = f(x), except shifted horizontally by h steps. - If h < 0, then f(x) is shifted right. - If k > 0, then f(x) is shifted left. Note that this seems opposite of what you d expect! For any function - y = f(x h) + k is the exact same shape as y = f(x), except shifted h spaces horizontally and k spaces vertically. Parabola (Vertex Form) - The function f(x) = (x h) 2 + k is a translation of f(x) = x 2. o Shifted h spaces horizontally and k spaces vertically. o The vertex is at (h, k) Example: Graph the function f(x) = (x + 3) 2 6 Start by finding the vertex: (-3, -6). Sketch a set of axes and plot the point. Plug in a few x-values to one side of the -3, noting that the symmetry of a parabola allows you to use only one side. Homework #2-10: Translation Practice

2 Algebra 2 Honors *Lesson #2-10 Name: Translating Functions Part 1: Vertical Shifts Fill in the table for f(x) and g(x). Then, graph each function on the axes. x f(x) = x 2 g(x) = x How do the g(x) values compare to the f(x) values? Calculator Part 1: Set your calculator window to the following: -6 < x < 6 and -3 < y < 6 Graph all of the following functions on the same screen. After you put in each new function, view the graph to see what it looks like. 1) Y 1 x 2 3) Y 3 x 2 2 5) Y 5 x 2 2 2) Y 2 x 2 1 4) Y 4 x 2 1 1) Based on your results, describe how adding or subtracting a number to f(x) = x 2 affects the graph. 2) Predict: what will the graph of f(x) = x look like? Check it on your calculator (you will need to change your viewing window).

3 Part 2: Horizontal Shifts Fill in the table for f(x) and g(x). Then, graph each function on the axes. x f(x) = x 2 g(x) = (x 2) How do the g(x) values compare to the f(x) values? Calculator Part 2: Set your calculator window to the following: -6 < x < 6 and -3 < y < 6 Graph all of the following functions on the same screen. After you put in each new function, view the graph to see what it looks like. 1) Y 1 x 2 3) Y 2 x 3 2) Y 2 x 1 2 4) Y 2 x ) Y 2 x 4 2 3) Based on your results, describe how adding or subtracting a number to the x before squaring affects the graph of f(x) = x 2. Is there anything surprising about it? 4) Predict: what will the graph of f(x) = (x + 7) 2 look like? Check it on your calculator (you will need to change your viewing window). 5) Synthesize: based on your results in part 1 and in part 2, what do you think the graph of f (x) x will look like? Graph it on your calculator to check. 6) Synthesize: Given that the vertex of f (x) x 2 is (0, 0), what will be the vertex of 2 k? f (x) x h

4 Algebra 2 Honors Lesson #2-10 Name: Homework #2-10: Translating Functions 1) Write the function whose graph is the same as the graph of y = x 2, but is translated: a. to the right 4 units. b. down 3 units. c. to the left 7.5 units. d. up units. e. to the right 3 and down 7 units. f. to the left 8 and up 8 units. 2) If (0, 3) is a point on the graph of y = f(x), which of the following points must be on the graph of y = f(x) + 5? a. (0, -2) b. (5, 3) c. (0, 8) d. (-5, 3) 3) If (7, 3) is a point on the graph of y = f(x), which of the following points must be on the graph of y = f(x + 3)? a. (4, 3) b. (11, 3) c. (7, 6) d. (7, 0) 4) If (-2, 8) is a point on the graph of y = f(x), which of the following points must be on the graph of y = f(x 2) + 4? a. (-4, 12) b. (-4, 4) c. (0, 4) d. (0, 12) 5) Write the function of each parabola on the graph. They are all translations of f(x) = x 2. a(x) = b(x) = c(x) = d(x) =

5 6) You are given the graph of y = f(x) below. On the same coordinate plane, graph the functions g(x), h(x), s(x), and t(x) using f(x) as a base. Use different colors for the different functions. g(x) = f(x) + 5 h(x) = f(x + 3) s(x) = f(x 4) t(x) = f(x 3) 6 7) Make a graph of each parabola. Do this by first finding and plotting the vertex, and then plug in a few x-values on one side of the vertex. Use symmetry to find points on the other side. 8) f (x) x g(x) x Vertex: (, ) Vertex: (, ) Hint: pick a point on the original function, and determine how it has moved to get to its new location. a. b. c. d.

6 Hw #2-9 Tally Sheet Page 1 1) 2) 3) 4) Page 2 Graph Problem) 1) 2) 3)

7 Hw #2-9 Answers 1) f (x) 3) f (x) Page 2: 2x 6, x 1 2x 6, x 1 6, 5 x 3 3x 12, x 3 2) f (x) 2x 5, x 0 0.5, 0 x 3 2 x 1, x 3 3 2x 16, x 3 4) f (x) 5, 3 x 2 4x 6, x 2 1) x = -1/3 or x = 5 2) -17 < x < 7 3) x < -3 or x > 8 Bonus: The lines intersect at (7, 25.5)

8 Part 1: Part 2:

. As x gets really large, the last terms drops off and f(x) ½x

. As x gets really large, the last terms drops off and f(x) ½x Pre-AP Algebra 2 Unit 8 -Lesson 3 End behavior of rational functions Objectives: Students will be able to: Determine end behavior by dividing and seeing what terms drop out as x Know that there will be

More information

Assignment Assignment for Lesson 9.1

Assignment Assignment for Lesson 9.1 Assignment Assignment for Lesson.1 Name Date Shifting Away Vertical and Horizontal Translations 1. Graph each cubic function on the grid. a. y x 3 b. y x 3 3 c. y x 3 3 2. Graph each square root function

More information

9.1: GRAPHING QUADRATICS ALGEBRA 1

9.1: GRAPHING QUADRATICS ALGEBRA 1 9.1: GRAPHING QUADRATICS ALGEBRA 1 OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator

More information

3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS

3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS 3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS Finding the Zeros of a Quadratic Function Examples 1 and and more Find the zeros of f(x) = x x 6. Solution by Factoring f(x) = x x 6 = (x 3)(x + )

More information

UNIT 3 EXPRESSIONS AND EQUATIONS Lesson 3: Creating Quadratic Equations in Two or More Variables

UNIT 3 EXPRESSIONS AND EQUATIONS Lesson 3: Creating Quadratic Equations in Two or More Variables Guided Practice Example 1 Find the y-intercept and vertex of the function f(x) = 2x 2 + x + 3. Determine whether the vertex is a minimum or maximum point on the graph. 1. Determine the y-intercept. The

More information

But a vertex has two coordinates, an x and a y coordinate. So how would you find the corresponding y-value?

But a vertex has two coordinates, an x and a y coordinate. So how would you find the corresponding y-value? We will work with the vertex, orientation, and x- and y-intercepts of these functions. Intermediate algebra Class notes More Graphs of Quadratic Functions (section 11.6) In the previous section, we investigated

More information

NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED

NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Algebra II (Wilsen) Midterm Review NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Remember: Though the problems in this packet are a good representation of many of the topics that will be on the exam, this

More information

Properties of Quadratic functions

Properties of Quadratic functions Name Today s Learning Goals: #1 How do we determine the axis of symmetry and vertex of a quadratic function? Properties of Quadratic functions Date 5-1 Properties of a Quadratic Function A quadratic equation

More information

Graphing Absolute Value Functions

Graphing Absolute Value Functions Graphing Absolute Value Functions To graph an absolute value equation, make an x/y table and plot the points. Graph y = x (Parent graph) x y -2 2-1 1 0 0 1 1 2 2 Do we see a pattern? Desmos activity: 1.

More information

Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is

Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is Algebra Review while 9 th graders are at Club Getaway 1-1 dist and mid pt cw. p. 4 (1,3,5,6,7,8, Hw p. 5 (1-10) Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is Find

More information

Polynomial and Rational Functions. Copyright Cengage Learning. All rights reserved.

Polynomial and Rational Functions. Copyright Cengage Learning. All rights reserved. 2 Polynomial and Rational Functions Copyright Cengage Learning. All rights reserved. 2.1 Quadratic Functions Copyright Cengage Learning. All rights reserved. What You Should Learn Analyze graphs of quadratic

More information

Unit 2: Function Transformation Chapter 1. Basic Transformations Reflections Inverses

Unit 2: Function Transformation Chapter 1. Basic Transformations Reflections Inverses Unit 2: Function Transformation Chapter 1 Basic Transformations Reflections Inverses Section 1.1: Horizontal and Vertical Transformations A transformation of a function alters the equation and any combination

More information

6.4 Vertex Form of a Quadratic Function

6.4 Vertex Form of a Quadratic Function 6.4 Vertex Form of a Quadratic Function Recall from 6.1 and 6.2: Standard Form The standard form of a quadratic is: f(x) = ax 2 + bx + c or y = ax 2 + bx + c where a, b, and c are real numbers and a 0.

More information

Transformations with Quadratic Functions KEY

Transformations with Quadratic Functions KEY Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting

More information

12.6. The Form Is Key. Vertex Form of a Quadratic Function

12.6. The Form Is Key. Vertex Form of a Quadratic Function The Form Is Key Vertex Form of a Quadratic Function.6 Learning Goals Key Term In this lesson, you will: Determine key characteristics of parabolas using a graphing calculator. Determine key characteristics

More information

Name: Chapter 7 Review: Graphing Quadratic Functions

Name: Chapter 7 Review: Graphing Quadratic Functions Name: Chapter Review: Graphing Quadratic Functions A. Intro to Graphs of Quadratic Equations: = ax + bx+ c A is a function that can be written in the form = ax + bx+ c where a, b, and c are real numbers

More information

Unit #3: Quadratic Functions Lesson #13: The Almighty Parabola. Day #1

Unit #3: Quadratic Functions Lesson #13: The Almighty Parabola. Day #1 Algebra I Unit #3: Quadratic Functions Lesson #13: The Almighty Parabola Name Period Date Day #1 There are some important features about the graphs of quadratic functions we are going to explore over the

More information

Lesson 3: Exploring Quadratic Relations Graphs Unit 5 Quadratic Relations

Lesson 3: Exploring Quadratic Relations Graphs Unit 5 Quadratic Relations (A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: How do we analyze and then work with a data set that shows both increase and decrease What is a parabola and what key features do they

More information

Assignments for Algebra 1 Unit 9 Quadratics, Part 1

Assignments for Algebra 1 Unit 9 Quadratics, Part 1 Name: Assignments for Algebra 1 Unit 9 Quadratics, Part 1 Day 1, Quadratic Transformations: p.1-2 Day 2, Vertex Form of Quadratics: p. 3 Day 3, Solving Quadratics: p. 4-5 Day 4, No Homework (be sure you

More information

MAFS Algebra 1. Quadratic Functions. Day 17 - Student Packet

MAFS Algebra 1. Quadratic Functions. Day 17 - Student Packet MAFS Algebra 1 Quadratic Functions Day 17 - Student Packet Day 17: Quadratic Functions MAFS.912.F-IF.3.7a, MAFS.912.F-IF.3.8a I CAN graph a quadratic function using key features identify and interpret

More information

Section a) f(x-3)+4 = (x 3) the (-3) in the parenthesis moves right 3, the +4 moves up 4

Section a) f(x-3)+4 = (x 3) the (-3) in the parenthesis moves right 3, the +4 moves up 4 Section 4.3 1a) f(x-3)+4 = (x 3) 2 + 4 the (-3) in the parenthesis moves right 3, the +4 moves up 4 Answer 1a: f(x-3)+4 = (x 3) 2 + 4 The graph has the same shape as f(x) = x 2, except it is shifted right

More information

Quadratics and their Properties

Quadratics and their Properties Algebra 2 Quadratics and their Properties Name: Ms. Williams/Algebra 2 Pd: 1 Table of Contents Day 1: COMPLETING THE SQUARE AND SHIFTING PARABOLAS SWBAT: Write a quadratic from standard form to vertex

More information

August 29, Quad2b FactoredForm Graphing.notebook

August 29, Quad2b FactoredForm Graphing.notebook Quadratics 2b Quadratic Function: Graphing Factored Form Standards: F IF.4 & F IF.7 GLOs: #3 Complex Thinker Math Practice: Look for and make use of structure HW: WS #9 (graph on graph paper!) Learning

More information

Module 3: Graphing Quadratic Functions

Module 3: Graphing Quadratic Functions Haberman MTH 95 Section V Quadratic Equations and Functions Module 3 Graphing Quadratic Functions In this module, we'll review the graphing quadratic functions (you should have studied the graphs of quadratic

More information

Algebra I. Slide 1 / 137. Slide 2 / 137. Slide 3 / 137. Quadratic & Non-Linear Functions. Table of Contents

Algebra I. Slide 1 / 137. Slide 2 / 137. Slide 3 / 137. Quadratic & Non-Linear Functions. Table of Contents Slide 1 / 137 Slide 2 / 137 Algebra I Quadratic & Non-Linear Functions 2015-11-04 www.njctl.org Table of Contents Slide 3 / 137 Click on the topic to go to that section Key Terms Explain Characteristics

More information

Warm-Up Exercises. Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; y = 2x + 7 ANSWER ; 7

Warm-Up Exercises. Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; y = 2x + 7 ANSWER ; 7 Warm-Up Exercises Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; 3 2. y = 2x + 7 7 2 ANSWER ; 7 Chapter 1.1 Graph Quadratic Functions in Standard Form A quadratic function is a function that

More information

Final Exam Review Algebra Semester 1

Final Exam Review Algebra Semester 1 Final Exam Review Algebra 015-016 Semester 1 Name: Module 1 Find the inverse of each function. 1. f x 10 4x. g x 15x 10 Use compositions to check if the two functions are inverses. 3. s x 7 x and t(x)

More information

Algebra II: Strand 3. Quadratic Functions; Topic 2. Digging Deeper; Task 3.2.1

Algebra II: Strand 3. Quadratic Functions; Topic 2. Digging Deeper; Task 3.2.1 1 TASK 3..1: PUTTING IT TOGETHER Solutions 1. Each of the following quadratic functions is given in standard form ( y = ax + bx + c ). For each function: Transform the function to the form y = a(x h) +

More information

Quadratic Functions Dr. Laura J. Pyzdrowski

Quadratic Functions Dr. Laura J. Pyzdrowski 1 Names: (8 communication points) About this Laboratory A quadratic function in the variable x is a polynomial where the highest power of x is 2. We will explore the domains, ranges, and graphs of quadratic

More information

F.BF.B.3: Graphing Polynomial Functions

F.BF.B.3: Graphing Polynomial Functions F.BF.B.3: Graphing Polynomial Functions 1 Given the graph of the line represented by the equation f(x) = 2x + b, if b is increased by 4 units, the graph of the new line would be shifted 4 units 1) right

More information

Do you need a worksheet or a copy of the teacher notes? Go to

Do you need a worksheet or a copy of the teacher notes? Go to Name Period Day Date Assignment (Due the next class meeting) Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday

More information

GSE Algebra 1 Name Date Block. Unit 3b Remediation Ticket

GSE Algebra 1 Name Date Block. Unit 3b Remediation Ticket Unit 3b Remediation Ticket Question: Which function increases faster, f(x) or g(x)? f(x) = 5x + 8; two points from g(x): (-2, 4) and (3, 10) Answer: In order to compare the rate of change (roc), you must

More information

Sample: Do Not Reproduce QUAD4 STUDENT PAGES. QUADRATIC FUNCTIONS AND EQUATIONS Student Pages for Packet 4: Quadratic Functions and Applications

Sample: Do Not Reproduce QUAD4 STUDENT PAGES. QUADRATIC FUNCTIONS AND EQUATIONS Student Pages for Packet 4: Quadratic Functions and Applications Name Period Date QUADRATIC FUNCTIONS AND EQUATIONS Student Pages for Packet 4: Quadratic Functions and Applications QUAD 4.1 Vertex Form of a Quadratic Function 1 Explore how changing the values of h and

More information

MEI Desmos Tasks for AS Pure

MEI Desmos Tasks for AS Pure Task 1: Coordinate Geometry Intersection of a line and a curve 1. Add a quadratic curve, e.g. y = x² 4x + 1 2. Add a line, e.g. y = x 3 3. Select the points of intersection of the line and the curve. What

More information

Function Transformations and Symmetry

Function Transformations and Symmetry CHAPTER Function Transformations and Symmetry The first well-documented postal system was in ancient Rome, where mail was carried by horsedrawn carriages and ox-drawn wagons. The US Postal Service delivers

More information

8-4 Transforming Quadratic Functions

8-4 Transforming Quadratic Functions 8-4 Transforming Quadratic Functions Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward

More information

Quadratic Functions. *These are all examples of polynomial functions.

Quadratic Functions. *These are all examples of polynomial functions. Look at: f(x) = 4x-7 f(x) = 3 f(x) = x 2 + 4 Quadratic Functions *These are all examples of polynomial functions. Definition: Let n be a nonnegative integer and let a n, a n 1,..., a 2, a 1, a 0 be real

More information

Unit: Quadratic Functions

Unit: Quadratic Functions Unit: Quadratic Functions Learning increases when you have a goal to work towards. Use this checklist as guide to track how well you are grasping the material. In the center column, rate your understand

More information

Quadratic Functions (Section 2-1)

Quadratic Functions (Section 2-1) Quadratic Functions (Section 2-1) Section 2.1, Definition of Polynomial Function f(x) = a is the constant function f(x) = mx + b where m 0 is a linear function f(x) = ax 2 + bx + c with a 0 is a quadratic

More information

Transformations: Translating Functions

Transformations: Translating Functions Math Objectives Students will vertically translate a function by adding a constant and write the appropriate symbolic representation for the translated function. Students will horizontally translate a

More information

) 2 + (y 2. x 1. y c x2 = y

) 2 + (y 2. x 1. y c x2 = y Graphing Parabola Parabolas A parabola is a set of points P whose distance from a fixed point, called the focus, is equal to the perpendicular distance from P to a line, called the directrix. Since this

More information

Start Fred Functions. Quadratic&Absolute Value Transformations. Graphing Piecewise Functions Intro. Graphing Piecewise Practice & Review

Start Fred Functions. Quadratic&Absolute Value Transformations. Graphing Piecewise Functions Intro. Graphing Piecewise Practice & Review Honors CCM2 Unit 6 Name: Graphing Advanced Functions This unit will get into the graphs of simple rational (inverse variation), radical (square and cube root), piecewise, step, and absolute value functions.

More information

POLYNOMIALS Graphing Polynomial Functions Common Core Standard

POLYNOMIALS Graphing Polynomial Functions Common Core Standard K Polynomials, Lesson 6, Graphing Polynomial Functions (r. 2018) POLYNOMIALS Graphing Polynomial Functions Common Core Standard Next Generation Standard F-BF.3 Identify the effect on the graph of replacing

More information

Quadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31

Quadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31 CHAPTER Quadratic Functions Arches are used to support the weight of walls and ceilings in buildings. Arches were first used in architecture by the Mesopotamians over 4000 years ago. Later, the Romans

More information

Notes Packet on Quadratic Functions and Factoring Graphing quadratic equations in standard form, vertex form, and intercept form.

Notes Packet on Quadratic Functions and Factoring Graphing quadratic equations in standard form, vertex form, and intercept form. Notes Packet on Quadratic Functions and Factoring Graphing quadratic equations in standard form, vertex form, and intercept form. A. Intro to Graphs of Quadratic Equations:! = ax + bx + c A is a function

More information

Math 2 Spring Unit 5 Bundle Transformational Graphing and Inverse Variation

Math 2 Spring Unit 5 Bundle Transformational Graphing and Inverse Variation Math 2 Spring 2017 Unit 5 Bundle Transformational Graphing and Inverse Variation 1 Contents Transformations of Functions Day 1... 3 Transformations with Functions Day 1 HW... 10 Transformations with Functions

More information

Pre-Calculus Mr. Davis

Pre-Calculus Mr. Davis Pre-Calculus 2016-2017 Mr. Davis How to use a Graphing Calculator Applications: 1. Graphing functions 2. Analyzing a function 3. Finding zeroes (or roots) 4. Regression analysis programs 5. Storing values

More information

Name. Center axis. Introduction to Conic Sections

Name. Center axis. Introduction to Conic Sections Name Introduction to Conic Sections Center axis This introduction to conic sections is going to focus on what they some of the skills needed to work with their equations and graphs. year, we will only

More information

5.3 Vertex Form of Quadratics 2017.notebook. October 20, Homework Answers:

5.3 Vertex Form of Quadratics 2017.notebook. October 20, Homework Answers: Homework Answers: 21. 23. 25. 27. 52. 69. 70. 71. 50. a. Vertex (315, 630) b. Domain: (0, 630) Range: (0, 630) c. 360 ft d. 630ft 1 Graph WARM UP 1) Find the vertex of the quadratic function: 2) Complete

More information

2/22/ Transformations but first 1.3 Recap. Section Objectives: Students will know how to analyze graphs of functions.

2/22/ Transformations but first 1.3 Recap. Section Objectives: Students will know how to analyze graphs of functions. 1 2 3 4 1.4 Transformations but first 1.3 Recap Section Objectives: Students will know how to analyze graphs of functions. 5 Recap of Important information 1.2 Functions and their Graphs Vertical line

More information

10.3 vertex and max values with comparing functions 2016 ink.notebook. March 14, Vertex and Max Value & Page 101.

10.3 vertex and max values with comparing functions 2016 ink.notebook. March 14, Vertex and Max Value & Page 101. 10.3 vertex and max values with comparing functions 2016 ink.notebook Page 101 Page 102 10.3 Vertex and Value and Comparing Functions Algebra: Transformations of Functions Page 103 Page 104 Lesson Objectives

More information

Yimin Math Centre. Year 10 Term 2 Homework. 3.1 Graphs in the number plane The minimum and maximum value of a quadratic function...

Yimin Math Centre. Year 10 Term 2 Homework. 3.1 Graphs in the number plane The minimum and maximum value of a quadratic function... Year 10 Term 2 Homework Student Name: Grade: Date: Score: Table of contents 3 Year 10 Term 2 Week 3 Homework 1 3.1 Graphs in the number plane................................. 1 3.1.1 The parabola....................................

More information

Honors Algebra 2 Function Transformations Discovery

Honors Algebra 2 Function Transformations Discovery Honors Algebra Function Transformations Discovery Name: Date: Parent Polynomial Graphs Using an input-output table, make a rough sketch and compare the graphs of the following functions. f x x. f x x.

More information

Lesson 8 Introduction to Quadratic Functions

Lesson 8 Introduction to Quadratic Functions Lesson 8 Introduction to Quadratic Functions We are leaving exponential and logarithmic functions behind and entering an entirely different world. As you work through this lesson, you will learn to identify

More information

Foundations of Math II

Foundations of Math II Foundations of Math II Unit 6b: Toolkit Functions Academics High School Mathematics 6.6 Warm Up: Review Graphing Linear, Exponential, and Quadratic Functions 2 6.6 Lesson Handout: Linear, Exponential,

More information

Section 3.3. Analyzing Graphs of Quadratic Functions

Section 3.3. Analyzing Graphs of Quadratic Functions Section 3.3 Analyzing Graphs of Quadratic Functions Introduction Definitions A quadratic function is a function with the form f (x) = ax 2 + bx + c, where a 0. Definitions A quadratic function is a function

More information

Y. Butterworth Lehmann & 9.2 Page 1 of 11

Y. Butterworth Lehmann & 9.2 Page 1 of 11 Pre Chapter 9 Coverage Quadratic (2 nd Degree) Form a type of graph called a parabola Form of equation we'll be dealing with in this chapter: y = ax 2 + c Sign of a determines opens up or down "+" opens

More information

MEI GeoGebra Tasks for AS Pure

MEI GeoGebra Tasks for AS Pure Task 1: Coordinate Geometry Intersection of a line and a curve 1. Add a quadratic curve, e.g. y = x 2 4x + 1 2. Add a line, e.g. y = x 3 3. Use the Intersect tool to find the points of intersection of

More information

Graph each function. State the domain, the vertex (min/max point), the range, the x intercepts, and the axis of symmetry.

Graph each function. State the domain, the vertex (min/max point), the range, the x intercepts, and the axis of symmetry. HW Worksheet Name: Graph each function. State the domain, the vertex (min/max point), the range, the x intercepts, and the axis of smmetr..) f(x)= x + - - - - x - - - - Vertex: Max or min? Axis of smmetr:.)

More information

a translation by c units a translation by c units

a translation by c units a translation by c units 1.6 Graphical Transformations Introducing... Translations 1.) Set your viewing window to [-5,5] by [-5,15]. 2.) Graph the following functions: y 1 = x 2 y 2 = x 2 + 3 y 3 = x 2 + 1 y 4 = x 2-2 y 5 = x

More information

Vertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once

Vertical Line Test a relationship is a function, if NO vertical line intersects the graph more than once Algebra 2 Chapter 2 Domain input values, X (x, y) Range output values, Y (x, y) Function For each input, there is exactly one output Example: Vertical Line Test a relationship is a function, if NO vertical

More information

WK # Given: f(x) = ax2 + bx + c

WK # Given: f(x) = ax2 + bx + c Alg2H Chapter 5 Review 1. Given: f(x) = ax2 + bx + c Date or y = ax2 + bx + c Related Formulas: y-intercept: ( 0, ) Equation of Axis of Symmetry: x = Vertex: (x,y) = (, ) Discriminant = x-intercepts: When

More information

2-9 Operations with Complex Numbers

2-9 Operations with Complex Numbers 2-9 Operations with Complex Numbers Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Express each number in terms of i. 1. 9i 2. Find each complex conjugate. 3. 4. Find each product. 5. 6. Objective

More information

2.2 Transformers: More Than Meets the y s

2.2 Transformers: More Than Meets the y s 10 SECONDARY MATH II // MODULE 2 STRUCTURES OF EXPRESSIONS 2.2 Transformers: More Than Meets the y s A Solidify Understanding Task Writetheequationforeachproblembelow.Useasecond representationtocheckyourequation.

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Chapter 3 Polynomial and Rational Functions Review sections as needed from Chapter 0, Basic Techniques, page 8. Refer to page 187 for an example of the work required on paper for all graded homework unless

More information

Unit 2 Day 5. Characteristics of Quadratic Functions

Unit 2 Day 5. Characteristics of Quadratic Functions Unit 2 Day 5 Characteristics of Quadratic Functions 1 Warm Up 1.) Jason and Jim jumped off a cliff into the ocean in Acapulco while vacationing. Jason s height as a function of time could be modeled by

More information

Section 4.1 Review of Quadratic Functions and Graphs (3 Days)

Section 4.1 Review of Quadratic Functions and Graphs (3 Days) Integrated Math 3 Name What can you remember before Chapter 4? Section 4.1 Review of Quadratic Functions and Graphs (3 Days) I can determine the vertex of a parabola and generate its graph given a quadratic

More information

Chapter 2: Polynomial and Rational Functions Power Standard #7

Chapter 2: Polynomial and Rational Functions Power Standard #7 Chapter 2: Polynomial and Rational s Power Standard #7 2.1 Quadratic s Lets glance at the finals. Learning Objective: In this lesson you learned how to sketch and analyze graphs of quadratic functions.

More information

Section 2.1 Graphs. The Coordinate Plane

Section 2.1 Graphs. The Coordinate Plane Section 2.1 Graphs The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of numbers to form

More information

Sections 3.5, : Quadratic Functions

Sections 3.5, : Quadratic Functions Week 7 Handout MAC 1105 Professor Niraj Wagh J Sections 3.5, 4.3-4.4: Quadratic Functions A function that can be written in the form f(x)= ax 2 +bx+c for real numbers a, b, and c, with a not equal to zero,

More information

Warm - Up. Sunday, February 1, HINT: plot points first then connect the dots. Draw a graph with the following characteristics:

Warm - Up. Sunday, February 1, HINT: plot points first then connect the dots. Draw a graph with the following characteristics: Warm - Up Sunday, February 1, 2015 Draw a graph with the following characteristics: Maximums at (-3,4) and (2,2) Minimum at (-1,-3) X intercepts at (-4,0), (-2,0), (1,0), and (3,0) Y intercept at (0,-2)

More information

Chapter 6 Practice Test

Chapter 6 Practice Test MPM2D Mr. Jensen Chapter 6 Practice Test Name: Standard Form 2 y= ax + bx+ c Factored Form y= a( x r)( x s) Vertex Form 2 y= a( x h) + k Quadratic Formula ± x = 2 b b 4ac 2a Section 1: Multiply Choice

More information

Algebra. Chapter 4: FUNCTIONS. Name: Teacher: Pd:

Algebra. Chapter 4: FUNCTIONS. Name: Teacher: Pd: Algebra Chapter 4: FUNCTIONS Name: Teacher: Pd: Table of Contents Day1: Chapter 4-1: Relations SWBAT: (1) Identify the domain and range of relations and functions (2) Match simple graphs with situations

More information

Amplifying an Instructional Task Algebra II Example

Amplifying an Instructional Task Algebra II Example Original Task The student is expected to write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening. A(4)(B) Write the equations

More information

Math Analysis Chapter 1 Notes: Functions and Graphs

Math Analysis Chapter 1 Notes: Functions and Graphs Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs; Section 1- Basics of Functions and Their Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian

More information

Objective. 9-4 Transforming Quadratic Functions. Graph and transform quadratic functions.

Objective. 9-4 Transforming Quadratic Functions. Graph and transform quadratic functions. Warm Up Lesson Presentation Lesson Quiz Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward. 1. y = x 2 + 3 2. y = 2x 2 x

More information

EXERCISE SET 10.2 MATD 0390 DUE DATE: INSTRUCTOR

EXERCISE SET 10.2 MATD 0390 DUE DATE: INSTRUCTOR EXERCISE SET 10. STUDENT MATD 090 DUE DATE: INSTRUCTOR You have studied the method known as "completing the square" to solve quadratic equations. Another use for this method is in transforming the equation

More information

Math 1113 Notes - Quadratic Functions

Math 1113 Notes - Quadratic Functions Math 1113 Notes - Quadratic Functions Philippe B. Laval Kennesaw State University September 7, 000 Abstract This handout is a review of quadratic functions. It includes a review of the following topics:

More information

Exploring Quadratic Graphs

Exploring Quadratic Graphs Exploring Quadratic Graphs The general quadratic function is y=ax 2 +bx+c It has one of two basic graphs shapes, as shown below: It is a symmetrical "U"-shape or "hump"-shape, depending on the sign of

More information

3.7.2 Transformations of Linear and Exponential Functions

3.7.2 Transformations of Linear and Exponential Functions Name: # Honors Coordinate Algebra: Period Ms. Pierre Date:.7. Transformations of Linear and Exponential Functions Warm Up On a map, Maple Street is represented by the function f(x) = x, and Highland Street

More information

5.1 Introduction to the Graphs of Polynomials

5.1 Introduction to the Graphs of Polynomials Math 3201 5.1 Introduction to the Graphs of Polynomials In Math 1201/2201, we examined three types of polynomial functions: Constant Function - horizontal line such as y = 2 Linear Function - sloped line,

More information

Standard Form v. Vertex Form

Standard Form v. Vertex Form Standard Form v. Vertex Form The Standard Form of a quadratic equation is:. The Vertex Form of a quadratic equation is where represents the vertex of an equation and is the same a value used in the Standard

More information

8.2 Graph and Write Equations of Parabolas

8.2 Graph and Write Equations of Parabolas 8.2 Graph and Write Equations of Parabolas Where is the focus and directrix compared to the vertex? How do you know what direction a parabola opens? How do you write the equation of a parabola given the

More information

College Algebra Extra Credit Worksheet

College Algebra Extra Credit Worksheet College Algebra Extra Credit Worksheet Fall 011 Math W1003 (3) Corrin Clarkson Due: Thursday, October 0 th, 011 1 Instructions Each section of this extra credit work sheet is broken into three parts. The

More information

Algebra II Quadratic Functions

Algebra II Quadratic Functions 1 Algebra II Quadratic Functions 2014-10-14 www.njctl.org 2 Ta b le o f C o n te n t Key Terms click on the topic to go to that section Explain Characteristics of Quadratic Functions Combining Transformations

More information

Section 4.4: Parabolas

Section 4.4: Parabolas Objective: Graph parabolas using the vertex, x-intercepts, and y-intercept. Just as the graph of a linear equation y mx b can be drawn, the graph of a quadratic equation y ax bx c can be drawn. The graph

More information

Mathematical Reasoning. Lesson 37: Graphing Quadratic Equations. LESSON 37: Graphing Quadratic Equations

Mathematical Reasoning. Lesson 37: Graphing Quadratic Equations. LESSON 37: Graphing Quadratic Equations LESSON 37: Graphing Quadratic Equations Weekly Focus: quadratic equations Weekly Skill: graphing Lesson Summary: For the warm-up, students will solve a problem about mean, median, and mode. In Activity

More information

Introduction to Quadratic Functions

Introduction to Quadratic Functions Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions.................

More information

Lesson 1: Analyzing Quadratic Functions

Lesson 1: Analyzing Quadratic Functions UNIT QUADRATIC FUNCTIONS AND MODELING Lesson 1: Analyzing Quadratic Functions Common Core State Standards F IF.7 F IF.8 Essential Questions Graph functions expressed symbolically and show key features

More information

Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics

Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics Math 2 Coordinate Geometry Part 3 Inequalities & Quadratics 1 DISTANCE BETWEEN TWO POINTS - REVIEW To find the distance between two points, use the Pythagorean theorem. The difference between x 1 and x

More information

1 Vertical and Horizontal

1 Vertical and Horizontal www.ck12.org Chapter 1. Vertical and Horizontal Transformations CHAPTER 1 Vertical and Horizontal Transformations Here you will learn about graphing more complex types of functions easily by applying horizontal

More information

Unit 5: Quadratic Functions

Unit 5: Quadratic Functions Unit 5: Quadratic Functions LESSON #5: THE PARABOLA GEOMETRIC DEFINITION DIRECTRIX FOCUS LATUS RECTUM Geometric Definition of a Parabola Quadratic Functions Geometrically, a parabola is the set of all

More information

Geometry and Spatial Reasoning

Geometry and Spatial Reasoning Geometry and Spatial Reasoning Activity: TEKS: Overview: Materials: Exploring Reflections (7.7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The

More information

Unit 2: Functions and Graphs

Unit 2: Functions and Graphs AMHS Precalculus - Unit 16 Unit : Functions and Graphs Functions A function is a rule that assigns each element in the domain to exactly one element in the range. The domain is the set of all possible

More information

Section 6.1: Quadratic Functions and their Characteristics Vertical Intercept Vertex Axis of Symmetry Domain and Range Horizontal Intercepts

Section 6.1: Quadratic Functions and their Characteristics Vertical Intercept Vertex Axis of Symmetry Domain and Range Horizontal Intercepts Lesson 6 Quadratic Functions and Equations Lesson 6 Quadratic Functions and Equations We are leaving exponential functions behind and entering an entirely different world. As you work through this lesson,

More information

Unit 8, Ongoing Activity, Little Black Book of Algebra II Properties

Unit 8, Ongoing Activity, Little Black Book of Algebra II Properties Unit 8, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 8 Conic Sections 8.1 Circle write the definition, provide examples of both the standard

More information

Caryn Loves Math 1

Caryn Loves Math 1 2011-2015 Caryn Loves Math 1 Piecewise-defined Functions Bundles By Caryn White Table of Contents Copy Right Information:... 3 Worksheets... 4 Evaluating Piecewise Functions (1)... 5 Evaluating Piecewise

More information

GUIDED NOTES 3.5 TRANSFORMATIONS OF FUNCTIONS

GUIDED NOTES 3.5 TRANSFORMATIONS OF FUNCTIONS GUIDED NOTES 3.5 TRANSFORMATIONS OF FUNCTIONS LEARNING OBJECTIVES In this section, you will: Graph functions using vertical and horizontal shifts. Graph functions using reflections about the x-axis and

More information

Math Analysis Chapter 1 Notes: Functions and Graphs

Math Analysis Chapter 1 Notes: Functions and Graphs Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian coordinate system) Practice: Label each on the

More information

Integrated Algebra A Packet 1

Integrated Algebra A Packet 1 Name Date Integrated Algebra A Packet 1 Lesson/Notes Homework Coordinate Plane HW #1 Connecting Points To Make Figures HW #2 Intro to Transformations/Translations HW #3 Reflections HW #4 Symmetry HW #5

More information