VERTEX FORM (OF A QUADRATIC FUNCTION) STANDARD FORM (OF A QUADRATIC FUNCTION) f(x) = a(x - p) 2 + q. f(x) = ax 2 + bx + c
|
|
- Gertrude Wilkins
- 5 years ago
- Views:
Transcription
1
2 VERTEX FORM (OF A QUADRATIC FUNCTION) f(x) = a(x - p) 2 + q STANDARD FORM (OF A QUADRATIC FUNCTION) f(x) = ax 2 + bx + c
3 Rewrite the equation in vertex form by completing the square. y = x 2 + 6x + 5 y = (x 2 + 6x) + 5 y = (x 2 + 6x + 9-9) + 5 y = (x 2 + 6x + 9) y = (x + 3) y = (x + 3) 2-4 (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2-2ab + b 2 Group the first two terms. Add and subtract the square of half the coefficient of the x-term. Group the perfect square trinomial. Rewrite as the square of a binomial. Simplify.
4 How can you solve quadratic equations of these form? VERTEX FORM (OF A QUADRATIC FUNCTION) f(x) = a(x - p) 2 + q 0 = a(x - p) 2 + q a(x - p) 2 + q = 0 STANDARD FORM (OF A QUADRATIC FUNCTION) f(x) = ax 2 + bx + c 0 = ax 2 + bx + c ax 2 + bx + c = 0
5 Solve x 2 9 = 0 x 2 = 9 x 2 = 9 x = ±3 x = 3 and x = 3 ax 2 + bx + c = 0 The roots are 3 and -3.
6 Solve (x 1) 2 49 = 0 (x 1) 2 = 49 a(x - p) 2 + q = 0 (x 1) 2 = 49 (x 1) = ±7 x 1 = ±7 x = ±7 + 1 x = = 8 and x = = -6 The roots are 8 and -6.
7 A wide-screen television has a diagonal measure of 42 in. The width of the screen is 16 in. more than the height. Determine the dimensions of the screen, to the nearest tenth of an inch.
8 A wide-screen television has a diagonal measure of 42 in. The width of the screen is 16 in. more than the height. Determine the dimensions of the screen, to the nearest tenth of an inch. h 2 + (h + 16) 2 = 42 2 h 2 + (h h + 256) = h h = h h = 1508 h h = 754 h h + 64 = (h + 8) 2 = 818 (h + 8) 2 = 818 h + 8 = ± 818 Draw a diagram. Let h represent the height of the screen. Then, h + 16 represents the width of the screen. Use the Pythagorean Theorem. Solve by Completing the Square
9 A wide-screen television has a diagonal measure of 42 in. The width of the screen is 16 in. more than the height. Determine the dimensions of the screen, to the nearest tenth of an inch. h 2 + (h + 16) 2 = 42 2 h 2 + (h h + 256) = h h = h h = 1508 h h = 754 Since the height of the screen cannot be negative, h = is an extraneous root. (A root that does not satisfy the initial restrictions on the variable) h h + 64 = (h + 8) 2 = 818 h = ± (h + 8) 2 = 818 h = and h = h + 8 = ± 818 h 20.6 in and h 36.6 in
10 A wide-screen television has a diagonal measure of 42 in. The width of the screen is 16 in. more than the height. Determine the dimensions of the screen, to the nearest tenth of an inch. h = ± h = and h = h 20.6 and h 36.6 Since the height of the screen cannot be negative, h = is an extraneous root. (A root that does not satisfy the initial restrictions on the variable) height 20.6 in and width = 36.6 in
11 The circular Canadian two-dollar coin consists of an aluminum and bronze core and a nickel outer ring. If the radius of the inner core is 0.84 cm and the area of the circular face of the coin is 1.96π cm 2, what is the width of the outer ring?
12 The circular Canadian two-dollar coin consists of an aluminum and bronze core and a nickel outer ring. If the radius of the inner core is 0.84 cm and the area of the circular face of the coin is 1.96π cm 2, what is the width of the outer ring?
13 Solve a Quadratic Equation by Completing the Square when a = 1. Confirm your answer(s) graphically. Express your answers to the nearest tenth. x 2 21 = 10x x x = 21 (x x ) = 21 (x x + 25) 25 = 21 (x + 5) 2 25 = 21 (x + 5) 2 = (x + 5) 2 = 46 (x + 5) 2 = 46 x + 5 = ± 46 x = ± 46 5 The roots are and x = x = and x =
14 Solve a Quadratic Equation by Completing the Square when a = 1. Confirm your answer(s) graphically. Express your answers to the nearest tenth. The roots are and x =
15 Solve a Quadratic Equation p 2-4p = 11 by Completing the Square when a = 1. Confirm your answer(s) graphically. Express your answers to the nearest tenth.
16 Solve a Quadratic Equation -2x 2 3x + 7 = 0 by Completing the Square when a 1. Confirm your answer(s) graphically. Express your answers to the nearest hundredth.
17 Solve a Quadratic Equation -2x 2 3x + 7 = 0 by Completing the Square when a 1. Confirm your answer(s) graphically. Express your answers to the nearest hundredth.
18 Solve a Quadratic Equation -2x 2 5x + 2 = 0 by Completing the Square when a 1. Confirm your answer(s) graphically. Express your answers to the nearest hundredth.
19 A defender kicks a soccer ball away from her own half. The path of the kicked soccer ball can be approximated by the quadratic function h(x) = -0.06x x , where x is the horizontal distance travelled, in metres, from the goal line and h is the height, in metres. a) You can determine the distance the soccer ball is from the goal line by solving the corresponding equation, -0.06x x = 0. How far is the soccer ball from the goal line when it is kicked? Express your answer to the nearest tenth of a metre. b) How far does the soccer ball travel before it hits the ground?
20 A defender kicks a soccer ball away from her own half. The path of the kicked soccer ball can be approximated by the quadratic function h(x) = -0.06x x , where x is the horizontal distance travelled, in metres, from the goal line and h is the height, in metres. a) You can determine the distance the soccer ball is from the goal line by solving the corresponding equation, -0.06x x = 0. How far is the soccer ball from the goal line when it is kicked? Express your answer to the nearest tenth of a metre.
21 A defender kicks a soccer ball away from her own half. The path of the kicked soccer ball can be approximated by the quadratic function h(x) = -0.06x x , where x is the horizontal distance travelled, in metres, from the goal line and h is the height, in metres. a) You can determine the distance the soccer ball is from the goal line by solving the corresponding equation, -0.06x x = 0. How far is the soccer ball from the goal line when it is kicked? Express your answer to the nearest tenth of a metre.
22 A defender kicks a soccer ball away from her own half. The path of the kicked soccer ball can be approximated by the quadratic function h(x) = -0.06x x , where x is the horizontal distance travelled, in metres, from the goal line and h is the height, in metres. b) How far does the soccer ball travel before it hits the ground?
23 CHAPTER 3 TEST REVIEW QUESTIONS OPages: OProblems: 3, 4, 6, 9, 12
4.1 Graphical Solutions of Quadratic Equations Date:
4.1 Graphical Solutions of Quadratic Equations Date: Key Ideas: Quadratic functions are written as f(x) = x 2 x 6 OR y = x 2 x 6. f(x) is f of x and means that the y value is dependent upon the value of
More information9-8 Completing the Square
In the previous lesson, you solved quadratic equations by isolating x 2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When
More information= (Type exponential notation with positive exponents)
1. Subtract. Simplify by collecting like radical terms if possible. 2 2 = (Simplify your answer) 2. Add. Simplify if possible. = (Simplify your answer) 3. Divide and simplify. = (Type exponential notation
More informationAlgebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block:
Algebra II Unit # Name: 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: (A) Background Skills - Simplifying Radicals To simplify a radical that is not a perfect square: 50 8 300 7 7 98 (B)
More informationMath 2 1. Lesson 4-5: Completing the Square. When a=1 in a perfect square trinomial, then. On your own: a. x 2 18x + = b.
Math 1 Lesson 4-5: Completing the Square Targets: I can identify and complete perfect square trinomials. I can solve quadratic equations by Completing the Square. When a=1 in a perfect square trinomial,
More informationControlling the Population
Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1
More informationName Date Class California Standards 17.0, Quadratic Equations and Functions. Step 2: Graph the points. Plot the ordered pairs from your table.
California Standards 17.0, 1.0 9-1 There are three steps to graphing a quadratic function. Graph y x 3. Quadratic Equations and Functions 6 y 6 y x y x 3 5 1 1 0 3 1 1 5 0 x 0 x Step 1: Make a table of
More information2. Write each number as a power of 10 using negative exponents.
Q Review 1. Simplify each expression. a. 1 0 b. 5 2 1 c. d. e. (7) 2 f. 6 1 g. 6 0 h. (12x) 2 i. 1 j. 6bc 0 0 8 k. (11x) 0 l. 2 2 9 m. m 8 p 0 n. 5a 2c k ( mn) o. p. 8 p 2m n q. 8 2 q r 5 r. (10a) b 0
More informationMath 521B Chapter 4 Test (33 marks) Name:
Math 521B Chapter 4 Test (33 marks) Name: Multiple Choice Identify the choice that best completes the statement or answers the question. (10 marks) 1. What are the x-intercepts of the quadratic function
More informationQuadratic Equations. Math 20-1 Chapter 4. General Outcome: Develop algebraic and graphical reasoning through the study of relations.
Math 20-1 Chapter 4 Quadratic Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations. Specific Outcomes: RF1. Factor polynomial expressions of the form: ax
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Define each term in our own words.. quadratic function. vertical motion Problem
More informationSolving Quadratic Equations
Solving Quadratic Equations MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: solve quadratic equations by factoring, solve quadratic
More information30S Pre-Calculus Final Exam Review Chapters 1-4
30S Pre-Calculus Final Exam Review Chapters 1 - Name: 30S Pre-Calculus Final Exam Formula Sheet 30S Pre-Calculus Exam Review- Chapter 1 Sequences and Series Multiple Choice Identify the choice that best
More information- a function that can be written in the standard form. - a form of a parabola where and (h, k) is the vertex
4-1 Quadratic Functions and Equations Objectives A2.A.REI.D.6 (formerly A-REI.D.11) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
More informationUnit 2 Quadratics. Mrs. Valentine Math 3
Unit 2 Quadratics Mrs. Valentine Math 3 2.1 Factoring and the Quadratic Formula Factoring ax 2 + bx + c when a = ±1 Reverse FOIL method Find factors of c that add up to b. Using the factors, write the
More informationCompleting the Square
5-7 Completing the Square TEKS FOCUS TEKS (4)(F) Solve quadratic and square root equations. TEKS (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace. Additional TEKS
More informationSubtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.
REVIEW EXAMPLES 1) Solve 9x + 16 = 0 for x. 9x + 16 = 0 9x = 16 Original equation. Subtract 16 from both sides. 16 x 9 Divide both sides by 9. 16 x Take the square root of both sides. 9 4 x i 3 Evaluate.
More informationSolving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and 2)
Solving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and ) In situations that involve quadratic functions, the interesting questions often require solving equations. For example,
More informationSolving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4
CC Algebra II HW #14 Name Period Row Date Solving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4 Section 3.1 In Exercises 3 12, solve the equation by graphing. (See Example
More informationQuadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents
Slide 1 / 200 Quadratic Functions Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic Equations
More informationQuadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200.
Slide 1 / 200 Quadratic Functions Slide 2 / 200 Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationSlide 1 / 200. Quadratic Functions
Slide 1 / 200 Quadratic Functions Key Terms Slide 2 / 200 Table of Contents Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationFind two positive factors of 24 whose sum is 10. Make an organized list.
9.5 Study Guide For use with pages 582 589 GOAL Factor trinomials of the form x 2 1 bx 1 c. EXAMPLE 1 Factor when b and c are positive Factor x 2 1 10x 1 24. Find two positive factors of 24 whose sum is
More informationUsing the Laws of Exponents to Simplify Rational Exponents
6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify
More information6.1 Solving Quadratic Equations by Factoring
6.1 Solving Quadratic Equations by Factoring A function of degree 2 (meaning the highest exponent on the variable is 2), is called a Quadratic Function. Quadratic functions are written as, for example,
More informationMaintaining Mathematical Proficiency
Chapter Maintaining Mathematical Proficiency Simplify the expression. 1. 8x 9x 2. 25r 5 7r r + 3. 3 ( 3x 5) + + x. 3y ( 2y 5) + 11 5. 3( h 7) 7( 10 h) 2 2 +. 5 8x + 5x + 8x Find the volume or surface area
More informationLESSON 11 PRACTICE PROBLEMS
LESSON 11 PRACTICE PROBLEMS 1. a. Determine the volume of each of the figures shown below. Round your answers to the nearest integer and include appropriate units of b. Determine the volume of each of
More informationFind the component form of with initial point A(1, 3) and terminal point B(1, 3). Component form = 1 1, 3 ( 3) (x 1., y 1. ) = (1, 3) = 0, 6 Subtract.
Express a Vector in Component Form Find the component form of with initial point A(1, 3) and terminal point B(1, 3). = x 2 x 1, y 2 y 1 Component form = 1 1, 3 ( 3) (x 1, y 1 ) = (1, 3) and ( x 2, y 2
More informationPolynomials: Adding, Subtracting, & Multiplying (5.1 & 5.2)
Polynomials: Adding, Subtracting, & Multiplying (5.1 & 5.) Determine if the following functions are polynomials. If so, identify the degree, leading coefficient, and type of polynomial 5 3 1. f ( x) =
More informationSolving Equations by Factoring. Solve the quadratic equation x 2 16 by factoring. We write the equation in standard form: x
11.1 E x a m p l e 1 714SECTION 11.1 OBJECTIVES 1. Solve quadratic equations by using the square root method 2. Solve quadratic equations by completing the square Here, we factor the quadratic member of
More informationMultiplication of Polynomials
Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is
More informationFor all questions, answer choice E. NOTA" means none of the above answers is correct.
For all questions, answer choice " means none of the above answers is correct. 1. The sum of the integers 1 through n can be modeled by a quadratic polynomial. What is the product of the non-zero coefficients
More informationUnit four review. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Unit four review Short Answer 1. Graph the quadratic function y = 3x 2 6x + 5. Use the graph to determine the zeros of the function if they exist. 2. For what values of k does
More information6.1 Quadratic Expressions, Rectangles, and Squares. 1. What does the word quadratic refer to? 2. What is the general quadratic expression?
Advanced Algebra Chapter 6 - Note Taking Guidelines Complete each Now try problem in your notes and work the problem 6.1 Quadratic Expressions, Rectangles, and Squares 1. What does the word quadratic refer
More informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationSummer Prep Packet for students entering Algebra 2
Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students
More informationevaluate functions, expressed in function notation, given one or more elements in their domains
Describing Linear Functions A.3 Linear functions, equations, and inequalities. The student writes and represents linear functions in multiple ways, with and without technology. The student demonstrates
More informationAlgebra I. Slide 1 / 175. Slide 2 / 175. Slide 3 / 175. Quadratics. Table of Contents Key Terms
Slide 1 / 175 Slide 2 / 175 Algebra I Quadratics 2015-11-04 www.njctl.org Key Terms Table of Contents Click on the topic to go to that section Slide 3 / 175 Characteristics of Quadratic Equations Transforming
More informationAlgebra I. Key Terms. Slide 1 / 175 Slide 2 / 175. Slide 3 / 175. Slide 4 / 175. Slide 5 / 175. Slide 6 / 175. Quadratics.
Slide 1 / 175 Slide / 175 Algebra I Quadratics 015-11-04 www.njctl.org Key Terms Slide 3 / 175 Table of Contents Click on the topic to go to that section Slide 4 / 175 Characteristics of Quadratic Equations
More information9.4 Start Thinking. 9.4 Warm Up. 9.4 Cumulative Review Warm Up. Use a graphing calculator to graph ( )
9.4 Start Thinking Use a graphing calculator to graph ( ) f x = x + 4x 1. Find the minimum of the function using the CALC feature on the graphing calculator. Explain the relationship between the minimum
More informationPolynomial Functions
Polynomial Functions Equations and Graphs Characteristics The Factor Theorem The Remainder Theorem http://www.purplemath.com/modules/polyends5.htm 1 A cross-section of a honeycomb has a pattern with one
More informationAlgebra I Quadratics
1 Algebra I Quadratics 2015-11-04 www.njctl.org 2 Key Terms Table of Contents Click on the topic to go to that section Characteristics of Quadratic Equations Transforming Quadratic Equations Graphing Quadratic
More informationTopic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3
Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring
More informationUNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS
UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS This unit investigates quadratic functions. Students study the structure of quadratic expressions and write quadratic expressions in equivalent forms.
More informationAdditional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property
Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators.
More informationQuadratic Functions and Equations
Quadratic Functions and Equations Quadratic Graphs and Their Properties Objective: To graph quadratic functions of the form y = ax 2 and y = ax 2 + c. Objectives I can identify a vertex. I can grapy y
More informationUnit 5 Test: 9.1 Quadratic Graphs and Their Properties
Unit 5 Test: 9.1 Quadratic Graphs and Their Properties Quadratic Equation: (Also called PARABOLAS) 1. of the STANDARD form y = ax 2 + bx + c 2. a, b, c are all real numbers and a 0 3. Always have an x
More informationCommon Core Algebra 2. Chapter 3: Quadratic Equations & Complex Numbers
Common Core Algebra 2 Chapter 3: Quadratic Equations & Complex Numbers 1 Chapter Summary: The strategies presented for solving quadratic equations in this chapter were introduced at the end of Algebra.
More informationApplied 30S Unit 1 Quadratic Functions
Applied 30S Unit 1 Quadratic Functions Mrs. Kornelsen Teulon Collegiate Institute Learning checklist Quadratics Learning increases when you have a goal to work towards. Use this checklist as guide to track
More information3.1 Solving Quadratic Equations by Factoring
3.1 Solving Quadratic Equations by Factoring A function of degree (meaning the highest exponent on the variable is ) is called a Quadratic Function. Quadratic functions are written as, for example, f(x)
More informationB. Complex number have a Real part and an Imaginary part. 1. written as a + bi some Examples: 2+3i; 7+0i; 0+5i
Section 11.8 Complex Numbers I. The Complex Number system A. The number i = -1 1. 9 and 24 B. Complex number have a Real part and an Imaginary part II. Powers of i 1. written as a + bi some Examples: 2+3i;
More informationIntermediate Algebra Final Exam Review
Intermediate Algebra Final Exam Review Note to students: The final exam for MAT10, MAT 11 and MAT1 will consist of 30 multiple-choice questions and a few open-ended questions. The exam itself will cover
More informationAlgebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials
Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +
More informationTo solve a radical equation, you must take both sides of an equation to a power.
Topic 5 1 Radical Equations A radical equation is an equation with at least one radical expression. There are four types we will cover: x 35 3 4x x 1x 7 3 3 3 x 5 x 1 To solve a radical equation, you must
More informationUnit 9: Quadratics Intercept Form
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic
More informationAccessible Topic - Topics accessible to visually impaired students using a screen reader.
Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334
More informationMCF3M1 Exam Review. 1. Which relation is not a function? a. c. b. d. 2. What is the range of the function?
MCF3M1 Exam Review 1. Which relation is not a function? 2. What is the range of the function? a. R = {1, 5, 4, 7} c. R = {1, 2, 3, 4, 5, 6, 7} b. R = {1, 2, 3, 6} d. R = {2, 5, 4, 7} 3. Which function
More informationMaintaining Mathematical Proficiency
Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h
More informationExponent Laws. a m a n = a m + n a m a n = a m n, a 0. ( ab) m = a m b m. ˆ m. = a m. a n = 1 a n, a 0. n n = a. Radicals. m a. n b Ë. m a. = mn.
Name:. Math 0- Formula Sheet Sequences and Series t n = t + ( n )d S n = n È t ÎÍ + ( n )d S n = n Ê Á t + t n ˆ t n = t r n Ê t r n ˆ Á S n =, r r S n = rt n t r, r S = t r, r Trigonometry Exponent Laws
More informationChapter 1 Notes: Quadratic Functions
19 Chapter 1 Notes: Quadratic Functions (Textbook Lessons 1.1 1.2) Graphing Quadratic Function A function defined by an equation of the form, The graph is a U-shape called a. Standard Form Vertex Form
More informationr r 30 y 20y 8 7y x 6x x 5x x 8x m m t 9t 12 n 4n r 17r x 9x m 7m x 7x t t 18 x 2x U3L1 - Review of Distributive Law and Factoring
UL - Review of Distributive Law and Factoring. Expand and simplify. a) (6mn )(-5m 4 n 6 ) b) -6x 4 y 5 z 7 (-x 7 y 4 z) c) (x 4) - (x 5) d) (y 9y + 5) 5(y 4) e) 5(x 4y) (x 5y) + 7 f) 4(a b c) 6(4a + b
More informationOn a separate sheet of paper, answer the following questions by showing ALL of your work.
Final Exam Review Cummulative Math 20-1 Ch.1 Sequence and Series Final Exam Review On a separate sheet of paper, answer the following questions by showing ALL of your work. 1. The common difference in
More information2. A man has a pocket full of change, but cannot make change for a dollar. What is the greatest value of coins he could have?
1 Let a, b be the two solutions to the equation x 2 3x + 1 = 0 Find a 3 + b 3 (A) 12 (B) 14 (C) 16 (D) 18 (E) 24 (D) The sum of the roots of ax 2 + bx + c = 0 is b/a and the product is c/a Therefore a
More informationPractice Test Questions Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Test Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which set of data is correct for this graph? 5 y 4 3 1 5 4 3 1 1 1 3 4 5 x 3 4
More information6.4. The Quadratic Formula. LEARN ABOUT the Math. Selecting a strategy to solve a quadratic equation. 2x 2 + 4x - 10 = 0
6.4 The Quadratic Formula YOU WILL NEED graphing calculator GOAL Understand the development of the quadratic formula, and use the quadratic formula to solve quadratic equations. LEARN ABOUT the Math Devlin
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationPERT Practice Test #2
Class: Date: PERT Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Ê 1. What is the quotient of 6y 6 9y 4 + 12y 2 ˆ Ê 3y 2 ˆ? a. 2y 4 + 3y
More information3.1. QUADRATIC FUNCTIONS AND MODELS
3.1. QUADRATIC FUNCTIONS AND MODELS 1 What You Should Learn Analyze graphs of quadratic functions. Write quadratic functions in standard form and use the results to sketch graphs of functions. Find minimum
More informationSolving Linear Equations
Solving Linear Equations Golden Rule of Algebra: Do unto one side of the equal sign as you will do to the other Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other
More informationChapter 5: Quadratic Functions
Section 5.1: Square Root Property #1-20: Solve the equations using the square root property. 1) x 2 = 16 2) y 2 = 25 3) b 2 = 49 4) a 2 = 16 5) m 2 = 98 6) d 2 = 24 7) x 2 = 75 8) x 2 = 54 9) (x 3) 2 =
More information5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
More informationAlgebra Quadratics Applications HW#54
Algebra Quadratics Applications HW#54 1: A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the
More informationName I.D. Number. Select the response that best completes the statement or answers the question.
Name I.D. Number Unit 4 Evaluation Evaluation 04 Second Year Algebra 1 (MTHH 039 059) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus,
More informationQuadratics in Factored Form Unit 2
1 U n i t 11C Date: Name: Tentative TEST date Quadratics in Factored Form Unit Reflect previous TEST mark, Overall mark now. Looking back, what can you improve upon? Learning Goals/Success Criteria Use
More informationHonors Algebra 2. a.) c.) d.) i and iv only. 3.) How many real roots must the following equation have? a.) 1 b.) 2 c.) 4 d.) none. a.) b.) c.) d.
Honors Algebra 2 The Polynomial Review Name: Date: Period: 1.) What is the remainder when p(x) = x 6 2x 3 + x 1 is divided by (x + 1)? 3 1 1 3 2.) If p(x) = x 3 2x 2 + 9x 2, which of the following statement(s)
More informationChapter 9 Quadratic Graphs
Chapter 9 Quadratic Graphs Lesson 1: Graphing Quadratic Functions Lesson 2: Vertex Form & Shifts Lesson 3: Quadratic Modeling Lesson 4: Focus and Directrix Lesson 5: Equations of Circles and Systems Lesson
More informationChapter 16 Review. 1. What is the solution set of n 2 + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n = { 2, 7} (D) n = { 2, 7} (E) n = { 7, 2}
Chapter 16 Review Directions: For each of the questions below, choose the best answer from the five choices given. 1. What is the solution set of n + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n =
More informationThe Quadratic Formula. ax 2 bx c 0 where a 0. Deriving the Quadratic Formula. Isolate the constant on the right side of the equation.
SECTION 11.2 11.2 The Quadratic Formula 11.2 OBJECTIVES 1. Solve quadratic equations by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation by using the discriminant
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.
More informationSection 1.7: Solving Equations by Factoring
Objective: Solve equations by factoring and using the zero product rule. When solving linear equations such as x 5 1, we can solve for the variable directly by adding 5 and dividing by to get 1. However,
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationQuadratic Equations CHAPTER 4
CHAPTER 4 Quadratic Equations What do water fountains, fireworks, satellite dishes, bridges, and model rockets have in common? They all involve a parabolic shape. You can develop and use quadratic equations
More informationQuadratics Unit Review
Name: Class: Date: Quadratics Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (2 points) Consider the graph of the equation y = ax 2 + bx +
More informationChapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand
Chapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand VOCAB: a quadratic function in standard form is written y = ax 2 + bx + c, where a 0 A quadratic Function creates
More informationQUADRATIC FUNCTIONS AND MODELS
QUADRATIC FUNCTIONS AND MODELS What You Should Learn Analyze graphs of quadratic functions. Write quadratic functions in standard form and use the results to sketch graphs of functions. Find minimum and
More informationDefinitions Term Description Examples Mixed radical the product of a monomial and a radical
Chapter 5 Radical Expressions and Equations 5.1 Working With Radicals KEY IDEAS Definitions Term Description Examples Mixed radical the product of a monomial and a radical index radical sign -8 45 coefficient
More informationCC Algebra Quadratic Functions Test Review. 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1?
Name: CC Algebra Quadratic Functions Test Review Date: 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1? a. c. c. b. d. Which statement best describes
More informationSolving Quadratic Equations Review
Math III Unit 2: Polynomials Notes 2-1 Quadratic Equations Solving Quadratic Equations Review Name: Date: Period: Some quadratic equations can be solved by. Others can be solved just by using. ANY quadratic
More informationQuadratic Equations CHAPTER 4
CHAPTER 4 Quadratic Equations What do water fountains, fireworks, satellite dishes, bridges, and model rockets have in common? They all involve a parabolic shape. You can develop and use quadratic equations
More information30 Wyner Math Academy I Fall 2015
30 Wyner Math Academy I Fall 2015 CHAPTER FOUR: QUADRATICS AND FACTORING Review November 9 Test November 16 The most common functions in math at this level are quadratic functions, whose graphs are parabolas.
More informationFinal Exam 2016 Practice Exam
Final Exam 2016 Practice Exam Short Answer 1. Multiply. 2. Multiply. 3. Find the product.. 4. Use the Quadratic Formula to solve. 5. Faye is 20 feet horizontally from the center of a basketball hoop that
More informationUNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS
UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS Act 1 Act 2 A rental car company charges $50.00 per day, plus $0.05 per mile driven. Write a function to model the story. How far did Angie drive if she rented
More informationUNIT 2 FACTORING. M2 Ch 11 all
UNIT 2 FACTORING M2 Ch 11 all 2.1 Polynomials Objective I will be able to put polynomials in standard form and identify their degree and type. I will be able to add and subtract polynomials. Vocabulary
More informationSection 5.5 Complex Numbers
Name: Period: Section 5.5 Comple Numbers Objective(s): Perform operations with comple numbers. Essential Question: Tell whether the statement is true or false, and justify your answer. Every comple number
More informationUNCC 2001 Algebra II
UNCC 2001 Algebra II March 5, 2001 1. Compute the sum of the roots of x 2 5x + 6 = 0. (A) 3 (B) 7/2 (C) 4 (D) 9/2 (E) 5 (E) The sum of the roots of the quadratic ax 2 + bx + c = 0 is b/a which, for this
More information6-2. Absolute Value, Square Roots, and Quadratic Equations. Vocabulary. Lesson. Example 1 Solve for x: x - 4 = 8.1. Mental Math
Chapter 6 Lesson 6-2 Absolute Value, Square Roots, and Quadratic Equations BIG IDEA Geometrically, the absolute value of a number is its distance on a number line from 0. Algebraically, the absolute value
More informationCUMULATIVE REVIEW (4 th Nine Weeks) Honors Algebra II Essential Question: What algebra skills should I possess when I leave Algebra II Honors?
Name Class/Period Date CUMULATIVE REVIEW (4 th Nine Weeks) Honors Algebra II Essential Question: What algebra skills should I possess when I leave Algebra II Honors? Directions: You will be assigned different
More informationAlgebra II Notes Quadratic Functions Unit Applying Quadratic Functions. Math Background
Applying Quadratic Functions Math Background Previously, you Graphed and solved quadratic functions. Solved literal equations for a given variable. Found the inverse for a linear function. Verified by
More informationUsing the binomial square thm. rewrite the following trinomial into an equivalent expression (The square of a binomial) 25c 2 70cd + 49d 2
Using the binomial square thm. rewrite the following trinomial into an equivalent expression (The square of a binomial) 25c 2 70cd + 49d 2 Dec 6 7:24 AM 1 Notes 6 1 Quadratic Expressions, Rectangles &
More informationMath League SCASD. Meet #5. Self-study Packet
Math League SCASD Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. Geometry: Solid Geometry (Volume and Surface Area)
More information