Mathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a.

Size: px
Start display at page:

Download "Mathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a."

Transcription

1 Mathematics 10 Page 1 of 7 Verte form of Quadratic Relations The epression a p q defines a quadratic relation called the verte form with a horizontal translation of p units and vertical translation of q units. The verte of the quadratic relation is p, q and ais of smmetr is at a. A quadratic relation in verte form a p q epanding and collecting like terms. can be converted to standard form a b c b a p q a p p 0 & q 0 Verte : a 0 p, q Ais of Smmetr : p Reflects about - ais Concaves down p, q p, q p 0 & q 0 Verte : p, q a 0 Concave up q Ais of Smmetr : p intercepts p q a intercept ap q Basic Points of a Quadratic Relation (Parabol Step Patterns: Eample 1: Parabola with a Vertical Translation Given the quadratic relation, determine the intercepts, intercept, direction of opening, ais of smmetr and the verte. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 4,

2 Mathematics 10 Page of 7 Eample : Parabola with a Horizontal Translation Given the quadratic relation, determine the intercepts, intercept, direction of opening, ais of smmetr and the verte. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 3, ,,

3 Mathematics 10 Page 3 of 7 Eample 3: Parabola with Translations Given the quadratic relation, determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 3, Eercise 1. Complete the chart: 4 7 e) 5 f) 1 verte -intercepts (if an) -intercept direction that curve opens equation of ais of smmetr. Graph the following equations on the same set of aes using the answers ou found in question 1. Label each parabola with its corresponding equation. e) f)

4 Mathematics 10 Page 4 of 7 3. Describe the effect of various values of "q" on the graph of q 4. Which graph best represents each of the following. (Label the graph with the appropriate letter) Write an equation that could correspond to each graph: a b c d 6. Fill in the following chart: 5 direction of opening coordinates of verte -intercepts (if an) -intercept For the general quadratic q : What are the co-ordinates of the verte? What restriction on the value of q eists in order for -intercepts to eist?

5 Mathematics 10 Page 5 of 7 8. Complete the chart for each equation. e) f) g) ( ) ( 4) ( 3) ( 6) ( 4) ( 6) verte equation of ais of smmetr -intercepts (if an) -intercept 9. Graph the following equations on the same set of aes using the answers ou found in question 8. Label each parabola with its corresponding equation. ( 3) f) ( 4) ( ) e) ( 6) g) ( 6) ( 4) 10. Compare the graphs of and ( p) when: p > 0 p < 0

6 Mathematics 10 Page 6 of Which graph best represents each of the following. Label with appropriate letter. ( 1) ( ) ( 4) ( 4) 1. Write an equation that could correspond to each graph: d c b a 13. Complete the following chart: co-ordinates of verte equation of ais of smmetr direction of opening -intercept (if an) -intercept ( 3) ( 8) ( ) e) ( 4)

7 Mathematics 10 Page 7 of 7 Answers 1 Verte: (0,0), -int: 0, -int: 0, opens up, = 0 Verte: (0,4), -int: NA, -int: 4, opens up, = 0 Verte: (0,7), -int: NA, -int: 7, opens up, = 0 Verte: (0,-), -int:, -int: -, opens up, = 0 e) Verte: (0,-5), -int: 5 -int: -5, opens up, = 0 f) Verte: (0,1), -int: NA, -int: 1, opens up, = 0 3) Vertical translations b q units a, d, c, b 4) 5) Opens up, Verte: (0,5), -int: NA, -int: 5 7 (0, q) q < 0 Opens up, Verte: (0,-3), -int: 3, -int: -3 Opens up, Verte: (0,), -int:na, -int: Opens up, Verte: (0,4), -int:na, -int: 4 8 Verte: (0,0), = 0, -int: 0, -int: p > 0 Right b p. Verte: (,0), =, -int:, -int: 4 p < 0 Left b p Verte: (-4,0), = -4, -int: -4, -int: 16 Verte: (-3,0), = -3, -int: -3, -int: 9 e) Verte: (6,0), = 6, -int: 6, -int: 36 f) Verte: (4,0), = 4, -int: 4, -int: 16 g) Verte: (-6,0), = -6, -int: -6, -int: ) ( 5) ( 1) ( 3) ( 6) c b a d 13 Verte: (0,0), = 0, opens up, -int: 0, -int: 0 Verte: (-3,0), = -3, opens up, -int: -3, -int: 9 Verte: (8,0), = 8, opens down, -int: 8, -int: -64 Verte: (,0), =, opens up, -int:, -int: 4 e) Verte: (-4,0), = -4, opens down, -int: -4, -int: -16

The coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.

The coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward. Mathematics 10 Page 1 of 8 Quadratic Relations in Vertex Form The expression y ax p q defines a quadratic relation in form. The coordinates of the of the corresponding parabola are p, q. If a > 0, the

More information

Vertex form of a quadratic equation

Vertex form of a quadratic equation Verte form of a quadratic equation Nikos Apostolakis Spring 017 Recall 1. Last time we looked at the graphs of quadratic equations in two variables. The upshot was that the graph of the equation: k = a(

More information

CHAPTER 3 : QUADRARIC FUNCTIONS MODULE CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions Graphs of quadratic functions 4 Eercis

CHAPTER 3 : QUADRARIC FUNCTIONS MODULE CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions Graphs of quadratic functions 4 Eercis ADDITIONAL MATHEMATICS MODULE 5 QUADRATIC FUNCTIONS CHAPTER 3 : QUADRARIC FUNCTIONS MODULE 5 3.1 CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions 3 3.3 Graphs of quadratic functions 4 Eercise

More information

3. TRANSLATED PARABOLAS

3. TRANSLATED PARABOLAS 3. TRANSLATED PARABOLAS The Parabola with Verte V(h, k) and Aes Parallel to the ais Consider the concave up parabola with verte V(h, k) shown below. This parabola is obtained b translating the parabola

More information

Section 2.5: Graphs of Functions

Section 2.5: Graphs of Functions Section.5: Graphs of Functions Objectives Upon completion of this lesson, ou will be able to: Sketch the graph of a piecewise function containing an of the librar functions. o Polnomial functions of degree

More information

QUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta

QUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape

More information

UNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x

UNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x 5A galler of graphs Objectives To recognise the rules of a number of common algebraic relations: = = = (rectangular hperbola) + = (circle). To be able to sketch the graphs of these relations. To be able

More information

Vertex Form of a Parabola

Vertex Form of a Parabola Verte Form of a Parabola In this investigation ou will graph different parabolas and compare them to what is known as the Basic Parabola. THE BASIC PARABOLA Equation = 2-3 -2-1 0 1 2 3 verte? What s the

More information

Rev Name Date. Solve each of the following equations for y by isolating the square and using the square root property.

Rev Name Date. Solve each of the following equations for y by isolating the square and using the square root property. Rev 8-8-3 Name Date TI-8 GC 3 Using GC to Graph Parabolae that are Not Functions of Objectives: Recall the square root propert Practice solving a quadratic equation f Graph the two parts of a hizontal

More information

STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs

STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic

More information

Lesson Goals. Unit 4 Polynomial/Rational Functions Quadratic Functions (Chap 0.3) Family of Quadratic Functions. Parabolas

Lesson Goals. Unit 4 Polynomial/Rational Functions Quadratic Functions (Chap 0.3) Family of Quadratic Functions. Parabolas Unit 4 Polnomial/Rational Functions Quadratic Functions (Chap 0.3) William (Bill) Finch Lesson Goals When ou have completed this lesson ou will: Graph and analze the graphs of quadratic functions. Solve

More information

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.

More information

AMB111F Notes 3 Quadratic Equations, Inequalities and their Graphs

AMB111F Notes 3 Quadratic Equations, Inequalities and their Graphs AMB111F Notes 3 Quadratic Equations, Inequalities and their Graphs The eqn y = a +b+c is a quadratic eqn and its graph is called a parabola. If a > 0, the parabola is concave up, while if a < 0, the parabola

More information

Modeling Revision Questions Set 1

Modeling Revision Questions Set 1 Modeling Revision Questions Set. In an eperiment researchers found that a specific culture of bacteria increases in number according to the formula N = 5 2 t, where N is the number of bacteria present

More information

recognise quadratics of the form y = kx 2 and y = (x + a) 2 + b ; a, b Î Z, from their graphs solve quadratic equations by factorisation

recognise quadratics of the form y = kx 2 and y = (x + a) 2 + b ; a, b Î Z, from their graphs solve quadratic equations by factorisation QUADRATIC FUNCTIONS B the end of this unit, ou should be able to: (a) (b) (c) (d) (e) recognise quadratics of the form = k 2 and = ( + a) 2 + b ; a, b Î Z, from their graphs identif the nature and coordinates

More information

Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.

Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots. Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to

More information

Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation

Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation Section -1 Functions Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation Definition: A rule that produces eactly one output for one input is

More information

Chapter XX: 1: Functions. XXXXXXXXXXXXXXX <CT>Chapter 1: Data representation</ct> 1.1 Mappings

Chapter XX: 1: Functions. XXXXXXXXXXXXXXX <CT>Chapter 1: Data representation</ct> 1.1 Mappings 978--08-8-8 Cambridge IGCSE and O Level Additional Mathematics Practice Book Ecerpt Chapter XX: : Functions XXXXXXXXXXXXXXX Chapter : Data representation This section will show you how to: understand

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.

More information

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic

More information

Lesson 4.1 Exercises, pages

Lesson 4.1 Exercises, pages Lesson 4.1 Eercises, pages 57 61 When approimating answers, round to the nearest tenth. A 4. Identify the y-intercept of the graph of each quadratic function. a) y = - 1 + 5-1 b) y = 3-14 + 5 Use mental

More information

Math RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus

Math RE - Calculus I Functions Page 1 of 10. Topics of Functions used in Calculus Math 0-03-RE - Calculus I Functions Page of 0 Definition of a function f() : Topics of Functions used in Calculus A function = f() is a relation between variables and such that for ever value onl one value.

More information

QUADRATIC FUNCTION REVIEW

QUADRATIC FUNCTION REVIEW Name: Date: QUADRATIC FUNCTION REVIEW Linear and eponential functions are used throughout mathematics and science due to their simplicit and applicabilit. Quadratic functions comprise another ver important

More information

Skills Practice Skills Practice for Lesson 1.1

Skills Practice Skills Practice for Lesson 1.1 Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +

More information

UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS

UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS Answer Key Name: Date: UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS Part I Questions. Which of the following is the value of 6? () 6 () 4 () (4). The epression is equivalent to 6 6 6 6 () () 6

More information

Writing Quadratic Functions in Standard Form

Writing Quadratic Functions in Standard Form Chapter Summar Ke Terms standard form (general form) of a quadratic function (.1) parabola (.1) leading coefficient (.) second differences (.) vertical motion model (.3) zeros (.3) interval (.3) open interval

More information

National 5 Mathematics

National 5 Mathematics St Andrew s Academ Mathematics Department National 5 Mathematics UNIT 4 ASSESSMENT PREPARATION St Andrew's Academ Maths Dept 016-17 1 Practice Unit Assessment 4A for National 5 1. Simplif, giving our answer

More information

Reteaching (continued)

Reteaching (continued) Quadratic Functions and Transformations If a, the graph is a stretch or compression of the parent function b a factor of 0 a 0. 0 0 0 0 0 a a 7 The graph is a vertical The graph is a vertical compression

More information

MATH section 3.4 Curve Sketching Page 1 of 29

MATH section 3.4 Curve Sketching Page 1 of 29 MATH section. Curve Sketching Page of 9 The step by step procedure below is for regular rational and polynomial functions. If a function contains radical or trigonometric term, then proceed carefully because

More information

Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula

Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula Mth 95 Module 4 Chapter 8 Spring 04 Review - Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b

More information

Quadratics NOTES.notebook November 02, 2017

Quadratics NOTES.notebook November 02, 2017 1) Find y where y = 2-1 and a) = 2 b) = -1 c) = 0 2) Epand the brackets and simplify: (m + 4)(2m - 3) To find the equation of quadratic graphs using substitution of a point. 3) Fully factorise 4y 2-5y

More information

17. f(x) = x 2 + 5x f(x) = x 2 + x f(x) = x 2 + 3x f(x) = x 2 + 3x f(x) = x 2 16x f(x) = x 2 + 4x 96

17. f(x) = x 2 + 5x f(x) = x 2 + x f(x) = x 2 + 3x f(x) = x 2 + 3x f(x) = x 2 16x f(x) = x 2 + 4x 96 Section.3 Zeros of the Quadratic 473.3 Eercises In Eercises 1-8, factor the given quadratic polnomial. 1. 2 + 9 + 14 2. 2 + 6 + 3. 2 + + 9 4. 2 + 4 21. 2 4 6. 2 + 7 8 7. 2 7 + 12 8. 2 + 24 In Eercises

More information

Lesson 9 Exploring Graphs of Quadratic Functions

Lesson 9 Exploring Graphs of Quadratic Functions Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point

More information

Using Intercept Form

Using Intercept Form 8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of

More information

LESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II

LESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also,

More information

Graphs and Solutions for Quadratic Equations

Graphs and Solutions for Quadratic Equations Format y = a + b + c where a 0 Graphs and Solutions for Quadratic Equations Graphing a quadratic equation creates a parabola. If a is positive, the parabola opens up or is called a smiley face. If a is

More information

Chapter 18 Quadratic Function 2

Chapter 18 Quadratic Function 2 Chapter 18 Quadratic Function Completed Square Form 1 Consider this special set of numbers - the square numbers or the set of perfect squares. 4 = = 9 = 3 = 16 = 4 = 5 = 5 = Numbers like 5, 11, 15 are

More information

20.2 Connecting Intercepts and Linear Factors

20.2 Connecting Intercepts and Linear Factors Name Class Date 20.2 Connecting Intercepts and Linear Factors Essential Question: How are -intercepts of a quadratic function and its linear factors related? Resource Locker Eplore Connecting Factors and

More information

Mathematics. Polynomials and Quadratics. hsn.uk.net. Higher. Contents. Polynomials and Quadratics 52 HSN22100

Mathematics. Polynomials and Quadratics. hsn.uk.net. Higher. Contents. Polynomials and Quadratics 52 HSN22100 Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 5 1 Quadratics 5 The Discriminant 54 Completing the Square 55 4 Sketching Parabolas 57 5 Determining the Equation

More information

4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2

4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2 COMMON CORE. d Locker d LESSON Parabolas Common Core Math Standards The student is epected to: COMMON CORE A-CED.A. Create equations in two or more variables to represent relationships between quantities;

More information

Saturday X-tra X-Sheet: 8. Inverses and Functions

Saturday X-tra X-Sheet: 8. Inverses and Functions Saturda X-tra X-Sheet: 8 Inverses and Functions Ke Concepts In this session we will ocus on summarising what ou need to know about: How to ind an inverse. How to sketch the inverse o a graph. How to restrict

More information

PACKET Unit 4 Honors ICM Functions and Limits 1

PACKET Unit 4 Honors ICM Functions and Limits 1 PACKET Unit 4 Honors ICM Functions and Limits 1 Day 1 Homework For each of the rational functions find: a. domain b. -intercept(s) c. y-intercept Graph #8 and #10 with at least 5 EXACT points. 1. f 6.

More information

Mathematics. Polynomials and Quadratics. hsn.uk.net. Higher. Contents. Polynomials and Quadratics 1. CfE Edition

Mathematics. Polynomials and Quadratics. hsn.uk.net. Higher. Contents. Polynomials and Quadratics 1. CfE Edition Higher Mathematics Contents 1 1 Quadratics EF 1 The Discriminant EF 3 3 Completing the Square EF 4 4 Sketching Parabolas EF 7 5 Determining the Equation of a Parabola RC 9 6 Solving Quadratic Inequalities

More information

QUADRATIC FUNCTIONS. ( x 7)(5x 6) = 2. Exercises: 1 3x 5 Sum: 8. We ll expand it by using the distributive property; 9. Let s use the FOIL method;

QUADRATIC FUNCTIONS. ( x 7)(5x 6) = 2. Exercises: 1 3x 5 Sum: 8. We ll expand it by using the distributive property; 9. Let s use the FOIL method; QUADRATIC FUNCTIONS A. Eercises: 1.. 3. + = + = + + = +. ( 1)(3 5) (3 5) 1(3 5) 6 10 3 5 6 13 5 = = + = +. ( 7)(5 6) (5 6) 7(5 6) 5 6 35 4 5 41 4 3 5 6 10 1 3 5 Sum: 6 + 10+ 3 5 ( + 1)(3 5) = 6 + 13 5

More information

Higher. Polynomials and Quadratics. Polynomials and Quadratics 1

Higher. Polynomials and Quadratics. Polynomials and Quadratics 1 Higher Mathematics Contents 1 1 Quadratics EF 1 The Discriminant EF 3 3 Completing the Square EF 4 4 Sketching Parabolas EF 7 5 Determining the Equation of a Parabola RC 9 6 Solving Quadratic Inequalities

More information

Section 3.3 Graphs of Polynomial Functions

Section 3.3 Graphs of Polynomial Functions 3.3 Graphs of Polynomial Functions 179 Section 3.3 Graphs of Polynomial Functions In the previous section we eplored the short run behavior of quadratics, a special case of polynomials. In this section

More information

Algebra I Quadratics Practice Questions

Algebra I Quadratics Practice Questions 1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 From CCSD CSE S Page 1 of 6 1 5. Which is equivalent

More information

Vertex. March 23, Ch 9 Guided Notes.notebook

Vertex. March 23, Ch 9 Guided Notes.notebook March, 07 9 Quadratic Graphs and Their Properties A quadratic function is a function that can be written in the form: Verte Its graph looks like... which we call a parabola. The simplest quadratic function

More information

f(x) = 2x 2 + 2x - 4

f(x) = 2x 2 + 2x - 4 4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms

More information

APPENDIX D Rotation and the General Second-Degree Equation

APPENDIX D Rotation and the General Second-Degree Equation APPENDIX D Rotation and the General Second-Degree Equation Rotation of Aes Invariants Under Rotation After rotation of the - and -aes counterclockwise through an angle, the rotated aes are denoted as the

More information

SAMPLE. A Gallery of Graphs. To recognise the rules of a number of common algebraic relationships: y = x 1,

SAMPLE. A Gallery of Graphs. To recognise the rules of a number of common algebraic relationships: y = x 1, Objectives C H A P T E R 5 A Galler of Graphs To recognise the rules of a number of common algebraic relationships: =, =, = / and + =. To be able to sketch the graphs and simple transformations of these

More information

Characteristics of Quadratic Functions

Characteristics of Quadratic Functions . Characteristics of Quadratic Functions Essential Question What tpe of smmetr does the graph of f() = a( h) + k have and how can ou describe this smmetr? Parabolas and Smmetr Work with a partner. a. Complete

More information

Coordinate geometry. + bx + c. Vertical asymptote. Sketch graphs of hyperbolas (including asymptotic behaviour) from the general

Coordinate geometry. + bx + c. Vertical asymptote. Sketch graphs of hyperbolas (including asymptotic behaviour) from the general A Sketch graphs of = a m b n c where m = or and n = or B Reciprocal graphs C Graphs of circles and ellipses D Graphs of hperbolas E Partial fractions F Sketch graphs using partial fractions Coordinate

More information

Math 3201 UNIT 5: Polynomial Functions NOTES. Characteristics of Graphs and Equations of Polynomials Functions

Math 3201 UNIT 5: Polynomial Functions NOTES. Characteristics of Graphs and Equations of Polynomials Functions 1 Math 301 UNIT 5: Polnomial Functions NOTES Section 5.1 and 5.: Characteristics of Graphs and Equations of Polnomials Functions What is a polnomial function? Polnomial Function: - A function that contains

More information

Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?

Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation? Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using

More information

Department of Mathematical and Statistical Sciences University of Alberta

Department of Mathematical and Statistical Sciences University of Alberta MATH 4 (R) Winter 8 Intermediate Calculus I Solutions to Problem Set #5 Completion Date: Frida Februar 5, 8 Department of Mathematical and Statistical Sciences Universit of Alberta Question. [Sec.., #

More information

Chapter 5: Systems of Equations and Inequalities. Section 5.4. Check Point Exercises

Chapter 5: Systems of Equations and Inequalities. Section 5.4. Check Point Exercises Chapter : Systems of Equations and Inequalities Section. Check Point Eercises. = y y = Solve the first equation for y. y = + Substitute the epression + for y in the second equation and solve for. ( + )

More information

14.3. Volumes of Revolution. Introduction. Prerequisites. Learning Outcomes

14.3. Volumes of Revolution. Introduction. Prerequisites. Learning Outcomes Volumes of Revolution 14.3 Introduction In this Section we show how the concept of integration as the limit of a sum, introduced in Section 14.1, can be used to find volumes of solids formed when curves

More information

4-1 Graphing Quadratic Functions

4-1 Graphing Quadratic Functions 4-1 Graphing Quadratic Functions Quadratic Function in standard form: f() a b c The graph of a quadratic function is a. y intercept Ais of symmetry -coordinate of verte coordinate of verte 1) f ( ) 4 a=

More information

12. Quadratics NOTES.notebook September 21, 2017

12. Quadratics NOTES.notebook September 21, 2017 1) Fully factorise 4y 2-5y - 6 Today's Learning: To find the equation of quadratic graphs using substitution of a point. 2) Epand the brackets and simplify: (m + 4)(2m - 3) 3) Calculate 20% of 340 without

More information

Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3

Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3 1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 Page 1 of 0 11 Practice Questions 6 1 5. Which

More information

7.2 Connecting Intercepts and Linear Factors

7.2 Connecting Intercepts and Linear Factors Name Class Date 7.2 Connecting Intercepts and Linear Factors Essential Question: How are -intercepts of a quadratic function and its linear factors related? Resource Locker Eplore Connecting Factors and

More information

Quadratic equationsgraphs

Quadratic equationsgraphs All reasonable efforts have been made to make sure the notes are accurate. The author cannot be held responsible for an damages arising from the use of these notes in an fashion. Quadratic equationsgraphs

More information

1.1 Laws of exponents Conversion between exponents and logarithms Logarithm laws Exponential and logarithmic equations 10

1.1 Laws of exponents Conversion between exponents and logarithms Logarithm laws Exponential and logarithmic equations 10 CNTENTS Algebra Chapter Chapter Chapter Eponents and logarithms. Laws of eponents. Conversion between eponents and logarithms 6. Logarithm laws 8. Eponential and logarithmic equations 0 Sequences and series.

More information

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k Name Class Date - Transforming Quadratic Functions Going Deeper Essential question: How can ou obtain the graph of g() = a( h ) + k from the graph of f () =? 1 F-BF..3 ENGAGE Understanding How to Graph

More information

Unit 2 Notes Packet on Quadratic Functions and Factoring

Unit 2 Notes Packet on Quadratic Functions and Factoring Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a

More information

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks) 1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of

More information

Section 4.1 Increasing and Decreasing Functions

Section 4.1 Increasing and Decreasing Functions Section.1 Increasing and Decreasing Functions The graph of the quadratic function f 1 is a parabola. If we imagine a particle moving along this parabola from left to right, we can see that, while the -coordinates

More information

NAME DATE PERIOD. Study Guide and Intervention. Transformations of Quadratic Graphs

NAME DATE PERIOD. Study Guide and Intervention. Transformations of Quadratic Graphs NAME DATE PERID Stud Guide and Intervention Write Quadratic Equations in Verte Form A quadratic function is easier to graph when it is in verte form. You can write a quadratic function of the form = a

More information

Lesson 10.1 Solving Quadratic Equations

Lesson 10.1 Solving Quadratic Equations Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One -intercept and all nonnegative y-values b. The verte in the third quadrant and no

More information

5.2 Solving Quadratic Equations by Factoring

5.2 Solving Quadratic Equations by Factoring Name. Solving Quadratic Equations b Factoring MATHPOWER TM, Ontario Edition, pp. 78 8 To solve a quadratic equation b factoring, a) write the equation in the form a + b + c = b) factor a + b + c c) use

More information

Mt. Douglas Secondary

Mt. Douglas Secondary Foundations of Math 11 Section 7.1 Quadratic Functions 31 7.1 Quadratic Functions Mt. Douglas Secondar Quadratic functions are found in everda situations, not just in our math classroom. Tossing a ball

More information

Quadratics in Vertex Form Unit 1

Quadratics in Vertex Form Unit 1 1 U n i t 1 11C Date: Name: Tentative TEST date Quadratics in Verte Form Unit 1 Reflect previous TEST mark, Overall mark now. Looking back, what can ou improve upon? Learning Goals/Success Criteria Use

More information

IB Questionbank Mathematical Studies 3rd edition. Quadratics. 112 min 110 marks. y l

IB Questionbank Mathematical Studies 3rd edition. Quadratics. 112 min 110 marks. y l IB Questionbank Mathematical Studies 3rd edition Quadratics 112 min 110 marks 1. The following diagram shows a straight line l. 10 8 y l 6 4 2 0 0 1 2 3 4 5 6 (a) Find the equation of the line l. The line

More information

RF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?

RF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct

More information

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 2201 MIDTERM EXAM JANUARY 2015 PART A: MULTIPLE CHOICE ANSWER SHEET

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 2201 MIDTERM EXAM JANUARY 2015 PART A: MULTIPLE CHOICE ANSWER SHEET QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 01 MIDTERM EXAM JANUARY 01 PART A: MULTIPLE CHOICE NAME: ANSWER SHEET 1. 11. 1.. 1... 1... 1... 1... 1.. 7. 17. 7. 8. 18. 8. 9. 19. 9. 10. 0. 0. QUADRATIC

More information

9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson

9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric

More information

Lesson 9.1 Using the Distance Formula

Lesson 9.1 Using the Distance Formula Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)

More information

The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.

The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope. LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find

More information

Quadratic Functions. The graph of the function shifts right 3. The graph of the function shifts left 3.

Quadratic Functions. The graph of the function shifts right 3. The graph of the function shifts left 3. Quadratic Functions The translation o a unction is simpl the shiting o a unction. In this section, or the most part, we will be graphing various unctions b means o shiting the parent unction. We will go

More information

UNCORRECTED SAMPLE PAGES. 3Quadratics. Chapter 3. Objectives

UNCORRECTED SAMPLE PAGES. 3Quadratics. Chapter 3. Objectives Chapter 3 3Quadratics Objectives To recognise and sketch the graphs of quadratic polnomials. To find the ke features of the graph of a quadratic polnomial: ais intercepts, turning point and ais of smmetr.

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=

More information

This problem set is a good representation of some of the key skills you should have when entering this course.

This problem set is a good representation of some of the key skills you should have when entering this course. Math 4 Review of Previous Material: This problem set is a good representation of some of the key skills you should have when entering this course. Based on the course work leading up to Math 4, you should

More information

TEST REVIEW QUADRATICS EQUATIONS Name: 2. Which of the following statements is true about the graph of the function?

TEST REVIEW QUADRATICS EQUATIONS Name: 2. Which of the following statements is true about the graph of the function? Chapter MATHEMATICS 00 TEST REVIEW QUADRATICS EQUATIONS Name:. Which equation does not represent a quadratic function?. Which of the following statements is true about the graph of the function? it has

More information

Lesson 5.1 Exercises, pages

Lesson 5.1 Exercises, pages Lesson 5.1 Eercises, pages 346 352 A 4. Use the given graphs to write the solutions of the corresponding quadratic inequalities. a) 2 2-8 - 10 < 0 The solution is the values of for which y

More information

Learning Targets: Standard Form: Quadratic Function. Parabola. Vertex Max/Min. x-coordinate of vertex Axis of symmetry. y-intercept.

Learning Targets: Standard Form: Quadratic Function. Parabola. Vertex Max/Min. x-coordinate of vertex Axis of symmetry. y-intercept. Name: Hour: Algebra A Lesson:.1 Graphing Quadratic Functions Learning Targets: Term Picture/Formula In your own words: Quadratic Function Standard Form: Parabola Verte Ma/Min -coordinate of verte Ais of

More information

Introduction to Rational Functions

Introduction to Rational Functions Introduction to Rational Functions The net class of functions that we will investigate is the rational functions. We will eplore the following ideas: Definition of rational function. The basic (untransformed)

More information

1 x

1 x Unit 1. Calculus Topic 4: Increasing and decreasing functions: turning points In topic 4 we continue with straightforward derivatives and integrals: Locate turning points where f () = 0. Determine the

More information

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

More information

Solve Quadratics Using the Formula

Solve Quadratics Using the Formula Clip 6 Solve Quadratics Using the Formula a + b + c = 0, = b± b 4 ac a ) Solve the equation + 4 + = 0 Give our answers correct to decimal places. ) Solve the equation + 8 + 6 = 0 ) Solve the equation =

More information

Path of the Horse s Jump y 3. transformation of the graph of the parent quadratic function, y 5 x 2.

Path of the Horse s Jump y 3. transformation of the graph of the parent quadratic function, y 5 x 2. - Quadratic Functions and Transformations Content Standards F.BF. Identif the effect on the graph of replacing f() b f() k, k f(), f(k), and f( k) for specific values of k (both positive and negative)

More information

6.3 Interpreting Vertex Form and Standard Form

6.3 Interpreting Vertex Form and Standard Form Name Class Date 6.3 Interpreting Verte Form and Standard Form Essential Question: How can ou change the verte form of a quadratic function to standard form? Resource Locker Eplore Identifing Quadratic

More information

10.4 Nonlinear Inequalities and Systems of Inequalities. OBJECTIVES 1 Graph a Nonlinear Inequality. 2 Graph a System of Nonlinear Inequalities.

10.4 Nonlinear Inequalities and Systems of Inequalities. OBJECTIVES 1 Graph a Nonlinear Inequality. 2 Graph a System of Nonlinear Inequalities. Section 0. Nonlinear Inequalities and Sstems of Inequalities 6 CONCEPT EXTENSIONS For the eercises below, see the Concept Check in this section.. Without graphing, how can ou tell that the graph of + =

More information

5-4. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING

5-4. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING 5- Focus and Directri of a Parabola TEKS FOCUS VOCABULARY TEKS ()(B) Write the equation of a parabola using given attributes, including verte, focus, directri, ais of smmetr, and direction of opening.

More information

Questions From Old Exams

Questions From Old Exams MATH 0 OLD EXAM QUESTIONS FOR EXAM 3 ON CHAPTERS 3 AND 4 PAGE Questions From Old Eams. Write the equation of a quadratic function whose graph has the following characteristics: It opens down; it is stretched

More information

Math 103 Final Exam Review Problems Rockville Campus Fall 2006

Math 103 Final Exam Review Problems Rockville Campus Fall 2006 Math Final Eam Review Problems Rockville Campus Fall. Define a. relation b. function. For each graph below, eplain why it is or is not a function. a. b. c. d.. Given + y = a. Find the -intercept. b. Find

More information

Answers. Investigation 2. ACE Assignment Choices. Applications. Problem 2.5. Problem 2.1. Problem 2.2. Problem 2.3. Problem 2.4

Answers. Investigation 2. ACE Assignment Choices. Applications. Problem 2.5. Problem 2.1. Problem 2.2. Problem 2.3. Problem 2.4 Answers Investigation ACE Assignment Choices Problem. Core, Problem. Core, Other Applications ; Connections, 3; unassigned choices from previous problems Problem.3 Core Other Connections, ; unassigned

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define

More information

Solve Quadratic Equations by Graphing

Solve Quadratic Equations by Graphing 0.3 Solve Quadratic Equations b Graphing Before You solved quadratic equations b factoring. Now You will solve quadratic equations b graphing. Wh? So ou can solve a problem about sports, as in Eample 6.

More information