2) f (x) = x 2 6x ) y = 1 2 (x 3)

Size: px
Start display at page:

Download "2) f (x) = x 2 6x ) y = 1 2 (x 3)"

Transcription

1 -- w lx0zts 0KuUtoaO Sqo5ftswa7rseL ULJLrCw.p FAlrlU ricghitssd jrieqshelr hvheydq.o n 5MoadweP OwgiFtthM BI7nnfuinNi7t7eH AglPgevbwrWan gf.t Worksheet b Kuta Software LLC Algebra /Trig ID: Name Graphing Quadratics 0U P KWuRtLai usuoaftthwmasrde mll0cn.c n TAilYl prciogqhwtesb urpedspegrov0edg.f Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. ) f () = 0 50 ) f () = + 0 3) f () = 3 ) = ( 3)

2 -- N OA0w3O ZK3uStPag vszoeftwwabrbem fllcf.c L JA0lNle OrEiRgbhFtGss hrmepsaesr YvAeZdk.A c fmuazdder oweiftkhi 9InUfi0nLiTtjeN JACligrewbfrUaK 7p.E Worksheet b Kuta Software LLC 5) = ( + ) + ) = ( 3) 7) = ( + 7)( 3) ) = ( + )( + )

3 -3- S B00C KwugtLa zs9orfytgw5air7e DLSLuCE.K d 0AlJlF JrijgwhNtmsv mrieasuervkerdo. g vmuadbej Yw7iStchc TIvnzfqiVnCiuteP Ajl3gue0bFreac YX.a Worksheet b Kuta Software LLC 9) = ( 3) 0) Verte: (, ), -intercept: 50 Use the information provided to write the verte form equation of each parabola. ) Verte: ( 9, 9), -intercept: 53 Use the information provided to write the intercept form equation of each parabola. ) Verte: (, ), -intercept: 0 Use the information provided to write the verte form equation of each parabola. 3) Opens up or down, Verte: ( 5, 0), Passes through: (, 9 ) ) Opens up or down, Verte: (, 9), Passes through: (0, )

4 -- d BZ0bm9 DKzutNas 5SGoUfntMw3aTrbei wlhlac.u OATlOls srbiwgkhmt5s MrReisue0r SvQedZ.G I KMAaTdZe uwointvh7 EIrnefTiTnwi0teM WALlsgOerberQa5 nv.v Worksheet b Kuta Software LLC Use the information provided to write the verte form equation of each parabola. 5) Use the information provided to write the intercept form equation of each parabola. ) )

5 -- Y mj07na VKuUtoa7 XSCoeftuwfamrEe5 0L0LWCC.V U 3AUlOlW r sihgxhitgsn Krqews5e7rqvAeQdu.W Z WM5adiew pwnigtwhn qi n5ffijnkimtzej AwlgJeBbqrkaN ga.n Worksheet b Kuta Software LLC Algebra /Trig ID: Name Graphing Quadratics q 9R0EUN zkgu St 5as PSjo5fztNwUaMreZ KLGLcCQ.i w raalilt DrGiMgchjtdsT trehsbelrqvkemd f.f Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. ) f () = 0 50 Verte: ( 5, 0) Ais of Sm.: = 5 Opens: Down Ma value = 0 -int: 50 -int: 5 ) f () = + 0 Verte: (3, ) Ais of Sm.: = 3 Min value = -int: 0 -int: None 3) f () = 3 Verte: (, 0) Ais of Sm.: = Opens: Down Ma value = 0 -int: 3 -int: ) = ( 3) Verte: (3, ) Ais of Sm.: = 3 Min value = -int: 7 -int: and 7

6 -- z c70m9 ikwuftwas SouftuwaorXe wlnlc.n a KAalhlu KrtiTgNhBtrsj vr7erszenrevxe0d7.z 9 BMacdsev IwSiltFhD sirnlffinhi0teew ZAXl7gLeVboriam LW.p Worksheet b Kuta Software LLC 5) = ( + ) + Verte: (, ) Ais of Sm.: = Min value = -int: -int: None ) = ( 3) Verte: (3, ) Ais of Sm.: = 3 Opens: Down Ma value = -int: 9 -int: None 7) = ( + 7)( 3) Verte: (, 5 ) Ais of Sm.: = Min value = 5 -int: -int: 7 and 3 ) = ( + )( + ) Verte: (, ) Ais of Sm.: = Opens: Down Ma value = -int: -int: and

7 -3- P P70oKA HKTuKtan msvo5fgt7wrar0e JLGLICJ. J sahljlq rrdipgph5tpsq 7rMeusegrVv3eadX.t J EM9apde FwOiath pionkfiijnxigtdev AA3l9gBeAbCrua9 gi.y Worksheet b Kuta Software LLC 9) = ( 3) Verte: (3, 0) Ais of Sm.: = 3 Min value = 0 -int: -int: 3 0) Verte: (, ), -intercept: 50 = Use the information provided to write the verte form equation of each parabola. ) Verte: ( 9, 9), -intercept: 53 = ( + 9) + 9 Use the information provided to write the intercept form equation of each parabola. ) Verte: (, ), -intercept: 0 = ( + ) Use the information provided to write the verte form equation of each parabola. 3) Opens up or down, Verte: ( 5, 0), Passes through: (, 9 ) = ( + 5) ) Opens up or down, Verte: (, 9), Passes through: (0, ) = 3

8 -- tf0jd kkvuctmaj 3SjomfEtUwca9rLeM ILjLwCL. r SAjljlk Cri9gQhStcst VrWecsTehrvOeCdH. G QMmadrep owhiut0hj BIBnAfqisnOitwe7 9AzlDgJehbzrab jh.v Worksheet b Kuta Software LLC Use the information provided to write the verte form equation of each parabola. 5) = ( ) Use the information provided to write the intercept form equation of each parabola. ) = ( + 3) 7) = + 7

REVIEW, pages

REVIEW, pages REVIEW, pages 69 697 8.. Sketch a graph of each absolute function. Identif the intercepts, domain, and range. a) = ƒ - + ƒ b) = ƒ ( + )( - ) ƒ 8 ( )( ) Draw the graph of. It has -intercept.. Reflect, in

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

Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( )

Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( ) Name Date 8. Practice A In Eercises 6, graph the function. Compare the graph to the graph of. g( ) =. h =.5 3. j = 3. g( ) = 3 5. k( ) = 6. n = 0.5 In Eercises 7 9, use a graphing calculator to graph the

More information

Graphing Quadratics: Vertex and Intercept Form

Graphing Quadratics: Vertex and Intercept Form Algebra : UNIT Graphing Quadratics: Verte and Intercept Form Date: Welcome to our second function famil...the QUADRATIC FUNCTION! f() = (the parent function) What is different between this function and

More information

GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM

GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 1 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM I) THE STANDARD FORM OF A QUADRATIC FUNCTION (PARABOLA) IS = a +b +c. To graph a quadratic function

More information

9.5 Graphing Quadratics- Parabolas

9.5 Graphing Quadratics- Parabolas Algebra G w0ka6o tkjuptnac asuoffzttwtarr]eg ]LGLXCX. q gaalxln lrxifgthftqsq Nrae_seXrcvveEdf. 9. Graphing Quadratics- Parabolas Name ID: Date Algebra Make sure each person in our group has a worksheet

More information

4.1 Graph Quadratic Functions in

4.1 Graph Quadratic Functions in 4. Graph Quadratic Functions in Standard Form Goal p Graph quadratic functions. Your Notes VOCABULARY Quadratic function Parabola Verte Ais of smmetr Minimum and maimum value PARENT FUNCTION FOR QUADRATIC

More information

Section 6.2: Properties of Graphs of Quadratic Functions. Vertex:

Section 6.2: Properties of Graphs of Quadratic Functions. Vertex: Section 6.2: Properties of Graphs of Quadratic Functions determine the vertex of a quadratic in standard form sketch the graph determine the y intercept, x intercept(s), the equation of the axis of symmetry,

More information

QUADRATIC FUNCTIONS Investigating Quadratic Functions in Vertex Form

QUADRATIC FUNCTIONS Investigating Quadratic Functions in Vertex Form QUADRATIC FUNCTIONS Investigating Quadratic Functions in Verte Form The two forms of a quadratic function that have been eplored previousl are: Factored form: f ( ) a( r)( s) Standard form: f ( ) a b c

More information

Unit 4 Part 1: Graphing Quadratic Functions. Day 1: Vertex Form Day 2: Intercept Form Day 3: Standard Form Day 4: Review Day 5: Quiz

Unit 4 Part 1: Graphing Quadratic Functions. Day 1: Vertex Form Day 2: Intercept Form Day 3: Standard Form Day 4: Review Day 5: Quiz Name: Block: Unit 4 Part 1: Graphing Quadratic Functions Da 1: Verte Form Da 2: Intercept Form Da 3: Standard Form Da 4: Review Da 5: Quiz 1 Quadratic Functions Da1: Introducing.. the QUADRATIC function

More information

10 Academic Date: Enter this equation into in DESMOS. Adjust your screen to show the scales like they are shown in the grid below.

10 Academic Date: Enter this equation into in DESMOS. Adjust your screen to show the scales like they are shown in the grid below. Academic Date: Open: DESMOS Graphing Calculator Task : Let s Review Linear Relationships Bill Bob s dog is out for a walk. The equation to model its distance awa from the house, d metres, after t seconds

More information

Example 1: Given below is the graph of the quadratic function f. Use the function and its graph to find the following: Outputs

Example 1: Given below is the graph of the quadratic function f. Use the function and its graph to find the following: Outputs Quadratic Functions: - functions defined by quadratic epressions (a 2 + b + c) o the degree of a quadratic function is ALWAYS 2 - the most common way to write a quadratic function (and the way we have

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

Algebra 1. 7 th Standard Complete Graphs. Categories Quadratic (p. 3-9) Exponential (p ) Absolute Value (p ) Linear (p.

Algebra 1. 7 th Standard Complete Graphs. Categories Quadratic (p. 3-9) Exponential (p ) Absolute Value (p ) Linear (p. Algebra 1 7 th Standard Complete Graphs Categories Quadratic (p. -9) Eponential (p. 10-1) Absolute Value (p. 14-17) Linear (p. 18-9) Summative Assessment Date: Wednesda, November 8 th Page 1 Standard:

More information

Worksheet: Transformations of Quadratic Functions

Worksheet: Transformations of Quadratic Functions Worksheet: Transformations of Quadratic Functions Multiple Choice Identif the choice that best completes the statement or answers the question.. Which correctl identifies the values of the parameters a,

More information

REVIEW, pages

REVIEW, pages REVIEW, pages 330 335 4.1 1. a) Use a table of values to graph = + 6-8. -5-4 -3 - -1 0 1 1 0-8 -1-1 -8 0 1 6 8 8 0 b) Determine: i) the intercepts ii) the coordinates of the verte iii) the equation of

More information

NOTES: ALGEBRA FUNCTION NOTATION

NOTES: ALGEBRA FUNCTION NOTATION STARTER: 1. Graph f by completing the table. f, y -1 0 1 4 5 NOTES: ALGEBRA 4.1 FUNCTION NOTATION y. Graph f 4 4 f 4 4, y --5-4 - - -1 0 1 y A Brief Review of Function Notation We will be using function

More information

Transformations of y = x 2

Transformations of y = x 2 Transformations of = Parent Parabola Lesson 11-1 Learning Targets: Describe translations of the parent function f() =. Given a translation of the function f() =, write the equation of the function. SUGGESTED

More information

8.5 Quadratic Functions and Their Graphs

8.5 Quadratic Functions and Their Graphs CHAPTER 8 Quadratic Equations and Functions 8. Quadratic Functions and Their Graphs S Graph Quadratic Functions of the Form f = + k. Graph Quadratic Functions of the Form f = - h. Graph Quadratic Functions

More information

Section 9.3: Functions and their Graphs

Section 9.3: Functions and their Graphs Section 9.: Functions and their Graphs Graphs provide a wa of displaing, interpreting, and analzing data in a visual format. In man problems, we will consider two variables. Therefore, we will need to

More information

Math 1050 Lab Activity: Graphing Transformations

Math 1050 Lab Activity: Graphing Transformations Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common

More information

Name w s2q0f1q7r XKkuxt[az usrodfxtdw^atruev hlglucz.s r katldli SrCifgshPtMsw tryems`e_rgviesdr.

Name w s2q0f1q7r XKkuxt[az usrodfxtdw^atruev hlglucz.s r katldli SrCifgshPtMsw tryems`e_rgviesdr. Precalculus Name w sq0f1q7r XKkut[az usrodftdw^atruev hlglucz.s r katldli SrCifgshPtMsw tryems`e_rgviesdr. Spring Final Review Solve each triangle. Round our answers to the nearest tenth. 1) ) B A 7 17

More information

3.1 Quadratic Functions in Vertex Form

3.1 Quadratic Functions in Vertex Form 3.1 Quadratic Functions in Vertex Form 1) Identify quadratic functions in vertex form. 2) Determine the effect of a, p, and q on the graph of a quadratic function in vertex form where y = a(x p)² + q 3)

More information

Worksheet A GRAPHS OF FUNCTIONS

Worksheet A GRAPHS OF FUNCTIONS C GRAPHS F FUNCTINS Worksheet A Sketch and label each pair of graphs on the same set of aes showing the coordinates of any points where the graphs intersect. Write down the equations of any asymptotes.

More information

Name: Date: Practice Final Exam Part II covering sections a108. As you try these problems, keep referring to your formula sheet.

Name: Date: Practice Final Exam Part II covering sections a108. As you try these problems, keep referring to your formula sheet. Name: Date: Practice Final Eam Part II covering sections 9.1-9.4 a108 As ou tr these problems, keep referring to our formula sheet. 1. Find the standard form of the equation of the circle with center at

More information

Graph the equation. 8) y = 6x - 2

Graph the equation. 8) y = 6x - 2 Math 0 Chapter Practice set The actual test differs. Write the equation that results in the desired transformation. 1) The graph of =, verticall compressed b a factor of 0.7 Graph the equation. 8) = -

More information

Graphs of quadratics functions are parabolas opening up if a > 0, and down if a < 0. Examples:

Graphs of quadratics functions are parabolas opening up if a > 0, and down if a < 0. Examples: Quadratic Functions ( ) = a + b + c Graphs o quadratics unctions are parabolas opening up i a > 0, and down i a < 0. Eamples: = = + = = 0 MATH 80 Lecture B o 5 Ronald Brent 07 All rights reserved. Notes:

More information

Lesson 8.1 Exercises, pages

Lesson 8.1 Exercises, pages Lesson 8.1 Eercises, pages 1 9 A. Complete each table of values. a) -3 - -1 1 3 3 11 8 5-1 - -7 3 11 8 5 1 7 To complete the table for 3, take the absolute value of each value of 3. b) - -3 - -1 1 3 3

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Begin b graphing the standard quadratic function f() =. Then use transformations of this

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

2. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0).

2. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0). Quadratics Vertex Form 1. Part of the graph of the function y = d (x m) + p is given in the diagram below. The x-intercepts are (1, 0) and (5, 0). The vertex is V(m, ). (a) Write down the value of (i)

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

Pre-Calculus 11: Final Review

Pre-Calculus 11: Final Review Pre-Calculus 11 Name: Block: FORMULAS Sequences and Series Pre-Calculus 11: Final Review Arithmetic: = + 1 = + or = 2 + 1 Geometric: = = or = Infinite geometric: = Trigonometry sin= cos= tan= Sine Law:

More information

Graphing Review. Math Tutorial Lab Special Topic

Graphing Review. Math Tutorial Lab Special Topic Graphing Review Math Tutorial Lab Special Topic Common Functions and Their Graphs Linear Functions A function f defined b a linear equation of the form = f() = m + b, where m and b are constants, is called

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

Properties of Graphs of Quadratic Functions

Properties of Graphs of Quadratic Functions H e i g h t (f t ) Lesson 2 Goal: Properties of Graphs of Quadratic Functions Identify the characteristics of graphs of quadratic functions: Vertex Intercepts Domain and Range Axis of Symmetry and use

More information

Parabolas Section 11.1

Parabolas Section 11.1 Conic Sections Parabolas Section 11.1 Verte=(, ) Verte=(, ) Verte=(, ) 1 3 If the equation is =, then the graph opens in the direction. If the equation is =, then the graph opens in the direction. Parabola---

More information

Name: Period: Date: Analyzing Graphs of Functions and Relations Guided Notes

Name: Period: Date: Analyzing Graphs of Functions and Relations Guided Notes Analzing Graphs of Functions and Relations Guided Notes The graph of a function f is the set of ordered pairs(, f ), in the coordinate plane, such that is the domain of f. the directed distance from the

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

GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS

GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS 1.1 DIFFERENT TYPES AND SHAPES OF GRAPHS: A graph can be drawn to represent are equation connecting two variables. There are different tpes of equations which

More information

Precalculus, IB Precalculus and Honors Precalculus

Precalculus, IB Precalculus and Honors Precalculus NORTHEAST CONSORTIUM Precalculus, IB Precalculus and Honors Precalculus Summer Pre-View Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help ou review topics from previous

More information

3.4 Reflections of Functions

3.4 Reflections of Functions 3. Reflections of Functions A coordinate grid is superimposed on a cross section of the Great Pramid, so that the -ais passes through the verte of the pramid. The -ais bisects two opposite sides of the

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

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

Answers Investigation 4

Answers Investigation 4 Answers Investigation Applications. a. At seconds, the flare will have traveled to a maimum height of 00 ft. b. The flare will hit the water when the height is 0 ft, which will occur at 0 seconds. c. In

More information

Quadratic Inequalities

Quadratic Inequalities TEKS FCUS - Quadratic Inequalities VCABULARY TEKS ()(H) Solve quadratic inequalities. TEKS ()(E) Create and use representations to organize, record, and communicate mathematical ideas. Representation a

More information

The simplest quadratic function we can have is y = x 2, sketched below.

The simplest quadratic function we can have is y = x 2, sketched below. Name: LESSON 6-8 COMPLETING THE SQUARE AND SHIFTING PARABOLAS COMMON CORE ALGEBRA II Date: Parabolas, and graphs more generall, can be moved horizontall and verticall b simple manipulations of their equations.

More information

10.2: Parabolas. Chapter 10: Conic Sections. Conic sections are plane figures formed by the intersection of a double-napped cone and a plane.

10.2: Parabolas. Chapter 10: Conic Sections. Conic sections are plane figures formed by the intersection of a double-napped cone and a plane. Conic sections are plane figures formed b the intersection of a double-napped cone and a plane. Chapter 10: Conic Sections Ellipse Hperbola The conic sections ma be defined as the sets of points in the

More information

Answers. Chapter 4. Cumulative Review Chapters 1 3, pp Chapter Self-Test, p Getting Started, p a) 49 c) e)

Answers. Chapter 4. Cumulative Review Chapters 1 3, pp Chapter Self-Test, p Getting Started, p a) 49 c) e) . 7" " " 7 "7.. "66 ( ") cm. a, (, ), b... m b.7 m., because t t has b ac 6., so there are two roots. Because parabola opens down and is above t-ais for small positive t, at least one of these roots is

More information

1.1 Horizontal & Vertical Translations

1.1 Horizontal & Vertical Translations Unit II Transformations of Functions. Horizontal & Vertical Translations Goal: Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related

More information

MATH 111 QUADRATICS WORKSHEET. Solution. We can put f(x) into vertex form by completing the square:

MATH 111 QUADRATICS WORKSHEET. Solution. We can put f(x) into vertex form by completing the square: MATH 111 QUADRATICS WORKSHEET BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA Name: Let f(x) = 3x 2 + 6x + 9. Use this function to answer questions Problems 1-3. 1. Write f(x) in vertex form. Solution. We can

More information

3x 2 + 7x + 2. A 8-6 Factor. Step 1. Step 3 Step 4. Step 2. Step 1 Step 2 Step 3 Step 4

3x 2 + 7x + 2. A 8-6 Factor. Step 1. Step 3 Step 4. Step 2. Step 1 Step 2 Step 3 Step 4 A 8-6 Factor. Step 1 3x 2 + 7x + 2 Step 2 Step 3 Step 4 3x 2 + 7x + 2 3x 2 + 7x + 2 Step 1 Step 2 Step 3 Step 4 Factor. 1. 3x 2 + 4x +1 = 2. 3x 2 +10x + 3 = 3. 3x 2 +13x + 4 = A 8-6 Name BDFM? Why? Factor.

More information

It s Not Complex Just Its Solutions Are Complex!

It s Not Complex Just Its Solutions Are Complex! It s Not Comple Just Its Solutions Are Comple! Solving Quadratics with Comple Solutions 15.5 Learning Goals In this lesson, ou will: Calculate comple roots of quadratic equations and comple zeros of quadratic

More information

Algebra 1: Quadratic Functions Review (Ch. 9 part 1)

Algebra 1: Quadratic Functions Review (Ch. 9 part 1) Name: Class: Date: ID: A Algebra 1: Quadratic Functions Review (Ch. 9 part 1) 1. Find the rule of a parabola that has the Ê 1 x-intercepts at ( 6,0) and,0 ˆ 3 ËÁ. 6. 2. Find the rule of a parabola that

More information

Problem 1: The relationship of height, in cm. and basketball players, names is a relation:

Problem 1: The relationship of height, in cm. and basketball players, names is a relation: Chapter - Functions and Graphs Chapter.1 - Functions, Relations and Ordered Pairs Relations A relation is a set of ordered pairs. Domain of a relation is the set consisting of all the first elements of

More information

Instructor: Virginia Davis Course: Foundations for College Math (1)

Instructor: Virginia Davis Course: Foundations for College Math (1) 5/19/01 Final Eam Review Ch 10,11-Virginia Davis Student: Date: Instructor: Virginia Davis Course: Foundations for College Math (1) Assignment: Final Eam Review Ch 10,11 1. Simplif b factoring. Assume

More information

Quadratic Functions and Factoring

Quadratic Functions and Factoring Chapter Quadratic Functions and Factoring Copright Houghton Mifflin Harcourt Publishing Compan. All rights reserved. Prerequisite Skills for the chapter Quadratic Functions and Factoring. The -intercept

More information

Using Characteristics of a Quadratic Function to Describe Its Graph. The graphs of quadratic functions can be described using key characteristics:

Using Characteristics of a Quadratic Function to Describe Its Graph. The graphs of quadratic functions can be described using key characteristics: Chapter Summar Ke Terms standard form of a quadratic function (.1) factored form of a quadratic function (.1) verte form of a quadratic function (.1) concavit of a parabola (.1) reference points (.) transformation

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

CHAPTER 9: Quadratic Equations and Functions

CHAPTER 9: Quadratic Equations and Functions Notes # CHAPTER : Quadratic Equations and Functions -: Exploring Quadratic Graphs A. Intro to Graphs of Quadratic Equations: = ax + bx + c A is a function that can be written in the form = ax + bx + c

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

2) The following data represents the amount of money Tom is saving each month since he graduated from college.

2) The following data represents the amount of money Tom is saving each month since he graduated from college. Mac 1 Review for Eam 3 Name(s) Solve the problem. 1) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1.8 and then add 3 to the result.

More information

Graphing f ( x) = ax 2 + c

Graphing f ( x) = ax 2 + c . Graphing f ( ) = a + c Essential Question How does the value of c affect the graph of f () = a + c? Graphing = a + c Work with a partner. Sketch the graphs of the functions in the same coordinate plane.

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 2: Function Transformation Chapter 1

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

More information

Unit 4: Part 1 Graphing Quadratic Functions

Unit 4: Part 1 Graphing Quadratic Functions Name: Block: Unit : Part 1 Graphing Quadratic Functions Da 1 Graphing in Verte Form & Intro to Quadratic Regression Da Graphing in Intercept Form Da 3 Da Da 5 Da Graphing in Standard Form Review Graphing

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

Investigating Transformations With DESMOS

Investigating Transformations With DESMOS MPM D0 Date: Investigating Transformations With DESMOS INVESTIGATION Part A: What if we add a constant to the x in y = x? 1. Use DESMOS to graph the following quadratic functions on the same grid. Graph

More information

1.1 Practice B. a. Without graphing, identify the type of function modeled by the equation.

1.1 Practice B. a. Without graphing, identify the type of function modeled by the equation. Name Date Name Date. Practice A. Practice B In Exercises and, identif the function famil to which f belongs. Compare the graph of f to the graph of its parent function... x f(x) = x In Exercises and, identif

More information

Transformations of Functions. 1. Shifting, reflecting, and stretching graphs Symmetry of functions and equations

Transformations of Functions. 1. Shifting, reflecting, and stretching graphs Symmetry of functions and equations Chapter Transformations of Functions TOPICS.5.. Shifting, reflecting, and stretching graphs Smmetr of functions and equations TOPIC Horizontal Shifting/ Translation Horizontal Shifting/ Translation Shifting,

More information

Sketching graphs of polynomials

Sketching graphs of polynomials Sketching graphs of polynomials We want to draw the graphs of polynomial functions y = f(x). The degree of a polynomial in one variable x is the highest power of x that remains after terms have been collected.

More information

Chapter Algebra 1 Copyright Big Ideas Learning, LLC Worked-Out Solutions. Maintaining Mathematical Proficiency.

Chapter Algebra 1 Copyright Big Ideas Learning, LLC Worked-Out Solutions. Maintaining Mathematical Proficiency. Chapter Maintaining Mathematical Proficienc. The function q is of the form = f(x h), where h =. So, the graph of q is a horizontal translation units left of the. The function h is of the form = af(x),

More information

Quadratic Functions Date: Per:

Quadratic Functions Date: Per: Math 2 Unit 10 Worksheet 1 Name: Quadratic Functions Date: Per: [1-3] Using the equations and the graphs from section B of the NOTES, fill out the table below. Equation Min or Max? Vertex Domain Range

More information

. 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

( )! 1! 3 = x + 1. ( ) =! x + 2

( )! 1! 3 = x + 1. ( ) =! x + 2 7.5 Graphing Parabolas 1. First complete the square: y = x 2 + 2x! 3 = x 2 + 2x + 1 ( )! 1! 3 = x + 1 ( ) 2! 4 The x-intercepts are 3,1 and the vertex is ( 1, 4). Graphing the parabola: 3. First complete

More information

Find the coordinates of the vertices of each figure after the given transformation. 4) reflection across y = 1

Find the coordinates of the vertices of each figure after the given transformation. 4) reflection across y = 1 Geometr i G2O01k4T AKduqtBaC QSMolfqtTwarrzej NLALtCS.I U AAblGld Vr_itghhFtosz frievs\enrrvze^dg. HW #9 - Reflections & Smmetr - amples A' ate eriod A 2) reflection across the -ais N(2, 2), (2, 3), (3,

More information

Lesson/Unit Plan Name: Comparing Linear and Quadratic Functions. Timeframe: 50 minutes + up to 60 minute assessment/extension activity

Lesson/Unit Plan Name: Comparing Linear and Quadratic Functions. Timeframe: 50 minutes + up to 60 minute assessment/extension activity Grade Level/Course: Algebra 1 Lesson/Unit Plan Name: Comparing Linear and Quadratic Functions Rationale/Lesson Abstract: This lesson will enable students to compare the properties of linear and quadratic

More information

Graphing Polynomial Functions

Graphing Polynomial Functions LESSON 7 Graphing Polnomial Functions Graphs of Cubic and Quartic Functions UNDERSTAND A parent function is the most basic function of a famil of functions. It preserves the shape of the entire famil.

More information

ABSOLUTE EXTREMA AND THE MEAN VALUE THEOREM

ABSOLUTE EXTREMA AND THE MEAN VALUE THEOREM 61 LESSON 4-1 ABSOLUTE EXTREMA AND THE MEAN VALUE THEOREM Definitions (informal) The absolute maimum (global maimum) of a function is the -value that is greater than or equal to all other -values in the

More information

Writing piecewise functions worksheet

Writing piecewise functions worksheet P ford residence southampton, ny Writing piecewise functions worksheet Cumulative Review. Cumulative Review 1-4 Answer Key. Cumulative Review Homework Answer Key. Unit 0: Review. Algebra 2 Trig Skills

More information

Final Exam Review. Name. Simplify. Your answer should contain only positive exponents.

Final Exam Review. Name. Simplify. Your answer should contain only positive exponents. 7 ccl9nejk nuz 8wBY6d Lcz7DPDtc R vzqazjub cwzudfmzo oovggrye ky Worksheet b Kuta Software LLC Final Eam Review k T6mUu 1fBgzr53 6 G DwFwBUffQIXb1p7hb Simplif. Your answer should contain onl positive eponents.

More information

Section 7.2 Characteristics of Quadratic Functions

Section 7.2 Characteristics of Quadratic Functions Section 7. Characteristics of Quadratic Functions A QUADRATIC FUNCTION is a function of the form " # $ N# 1 & ;# & 0 Characteristics Include:! Three distinct terms each with its own coefficient:! An x

More information

Shape and Structure. Forms of Quadratic Functions. Lesson 4.1 Skills Practice. Vocabulary

Shape and Structure. Forms of Quadratic Functions. Lesson 4.1 Skills Practice. Vocabulary Lesson.1 Skills Practice Name Date Shape and Structure Forms of Quadratic Functions Vocabular Write an eample for each form of quadratic function and tell whether the form helps determine the -intercepts,

More information

Graphing f ( x) = ax 2

Graphing f ( x) = ax 2 . Graphing f ( ) = a Essential Question What are some of the characteristics of the graph of a quadratic function of the form f () = a? Graphing Quadratic Functions Work with a partner. Graph each quadratic

More information

Laboratory One Distance and Time

Laboratory One Distance and Time Laboratory One Distance and Time Student Laboratory Description Distance and Time I. Background When an object is propelled upwards, its distance above the ground as a function of time is described by

More information

Quadratics Functions: Review

Quadratics Functions: Review Quadratics Functions: Review Name Per Review outline Quadratic function general form: Quadratic function tables and graphs (parabolas) Important places on the parabola graph [see chart below] vertex (minimum

More information

2.1 Transformers: Shifty y s A Develop Understanding Task

2.1 Transformers: Shifty y s A Develop Understanding Task 3 2.1 Transformers: Shifty y s A Develop Understanding Task Optima is designing a robot quilt for her new grandson. She plans for the robot to have a square face. The amount of fabric that she needs for

More information

a) A(5,7) and B(3,9) b) E( 1, 4) and F( 2,8) 2) find the equation of the line, in the form y=mx+b, that goes through the points: y = mx + b

a) A(5,7) and B(3,9) b) E( 1, 4) and F( 2,8) 2) find the equation of the line, in the form y=mx+b, that goes through the points: y = mx + b .1 medians DO IT NOW.1 Median of a Triangle 1) Determine the coordinates of the midpoint of the line segment defined by each pair of endpoints: a) A(5,7) and B(3,9) b) E( 1, 4) and F(,8) ) find the equation

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

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

Study Skills Exercise. Review Exercises. Concept 1: Linear and Constant Functions

Study Skills Exercise. Review Exercises. Concept 1: Linear and Constant Functions Section. Graphs of Functions Section. Boost our GRADE at mathzone.com! Stud Skills Eercise Practice Eercises Practice Problems Self-Tests NetTutor e-professors Videos. Define the ke terms. a. Linear function

More information

Worksheet #1 Fractions

Worksheet #1 Fractions Worksheet # Fractions " Evaluate each expression and leave your answer in simplest form. ] 7 ] = ] + 8 ] + ] 7 ] 7 8 + 7] 7 8] 8 9] 8 0] 9 0 ] ] 9 ] 0 #" Worksheet # Simplifying/Evaluating Expressions

More information

REMARKS. 8.2 Graphs of Quadratic Functions. A Graph of y = ax 2 + bx + c, where a > 0

REMARKS. 8.2 Graphs of Quadratic Functions. A Graph of y = ax 2 + bx + c, where a > 0 8. Graphs of Quadratic Functions In an earlier section, we have learned that the graph of the linear function = m + b, where the highest power of is 1, is a straight line. What would the shape of the graph

More information

TIPS4RM: MHF4U: Unit 1 Polynomial Functions

TIPS4RM: MHF4U: Unit 1 Polynomial Functions TIPSRM: MHFU: Unit Polnomial Functions 008 .5.: Polnomial Concept Attainment Activit Compare and contrast the eamples and non-eamples of polnomial functions below. Through reasoning, identif attributes

More information

Lesson 5.3 Exercises, pages

Lesson 5.3 Exercises, pages Lesson 5.3 Eercises, pages 37 3 A. Determine whether each ordered pair is a solution of the quadratic inequalit: 3 - a) (-3, ) b) (, 5) Substitute each ordered pair in» 3. L.S. ; R.S.: 3( 3) 3 L.S. 5;

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

( r, i ) Price of Bread ($) Date: Name: 4. What are the vertex and v intercept of the quadratic function f(x) = 2 + 3x 3x2? page 1

( r, i ) Price of Bread ($) Date: Name: 4. What are the vertex and v intercept of the quadratic function f(x) = 2 + 3x 3x2? page 1 Name: Date: 1. The area of a rectangle in square inches is represented by the epression 2 + 2 8. The length of the rectangle is + 4 inches. What is an epression for the width of the rectangle in inches?

More information

Review for Algebra 1 Final Exam 2016

Review for Algebra 1 Final Exam 2016 Name: Date: Period: Algebra 1 Bowling, Davis, Fletcher, Hale, Hernandez, Skiles Review for Algebra 1 Final Eam 016 1. What is the verte of the quadratic function to the right?. Which of the following quadratic

More information

Unit 2 Functions Analyzing Graphs of Functions (Unit 2.2)

Unit 2 Functions Analyzing Graphs of Functions (Unit 2.2) Unit 2 Functions Analzing Graphs of Functions (Unit 2.2) William (Bill) Finch Mathematics Department Denton High School Introduction Domain/Range Vert Line Zeros Incr/Decr Min/Ma Avg Rate Change Odd/Even

More information

1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1

1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1 .7 Transformations.7. Eercises To see all of the help resources associated with this section, click OSttS Chapter b. Suppose (, ) is on the graph of = f(). In Eercises - 8, use Theorem.7 to find a point

More information