Name Class Date. Identify the vertex of each graph. Tell whether it is a minimum or a maximum.
|
|
- Robert Wells
- 5 years ago
- Views:
Transcription
1 Practice Quadratic Graphs and Their Properties Identify the verte of each graph. Tell whether it is a minimum or a maimum. 1. y 2. y y Graph each function. 4. f () = f () = f () = Order each group of quadratic functions from widest to narrowest graph. 7. y = -3 2, y = -5 2, y = y = 4 2, y = -2 2, y = y = 2, y = 1 3 2, y = y = 1 6 2, y = 1 4 2, y = Graph each function. 11. f () = f () = f () = f () = f () = f () =
2 Practice (continued) Quadratic Graphs and Their Properties 17. For a physics eperiment, the class drops a golf ball off a bridge toward the pavement below. The bridge is 75 feet high. The function h = -16t gives the golf ball s height h above the pavement (in feet) after t seconds. Graph the function. How many seconds does it take for the golf ball to hit the pavement? 18. A relief organization flew over a village and dropped a package of food and medicine. The plane is flying at 1000 feet. The function h = -16t gives the package s height h above the ground (in feet) after t seconds. Graph the function. How many seconds does it take for the package to hit the ground? Identify the domain and range of each function. 19. y = y = y = f () = Use a graphing calculator to graph each function. Identify the verte and ais of symmetry. 23. y = y = y = Writing Discuss how the function y = differs from the graph y = Writing Eplain how you can determine if the parabola opens up or down by simply eamining the equation.
3 Practice Quadratic Functions Find the equation of the ais of symmetry and the coordinates of the verte of the graph of each function. 1. y = y = y = y = y = y = y = y = y = Graph each function. Label the ais of symmetry and the verte. 10. f () = f () = f () = f () = f () = f () = A punter kicked the football into the air with an upward velocity of 62 ft/s. Its height h in feet after t seconds is given by the function h = -16t t + 2. What is the maimum height the ball reaches? How long will it take the football to reach the maimum height? How long does it take for the ball to hit the ground? 17. A disc is thrown into the air with an upward velocity of 20 ft/s. Its height h in feet after t seconds is given by the function h = -16t t + 6. What is the maimum height the disc reaches? How long will it take the disc to reach the maimum height? How long does it take for the disc to be caught 3 feet off the ground?
4 Practice (continued) Quadratic Functions Graph each function. Label the ais of symmetry and the verte. 18. f () = f () = f () = f () = f () = f () = Open-Ended For Eercises 24 26, give an eample of a quadratic function with the given characteristic(s). 24. Its graph opens up and has its verte at (0, -3). 25. Its graph lies entirely below the -ais. 26. Its verte lies on the -ais and the graph opens down. 27. A fountain that is 5 feet tall sprays water into the air with an upward velocity of 22 ft/s. What function gives the height h of the water in feet t seconds after it is sprayed upward? What is the maimum height of the water? 28. The parabola shown at the right is of the form y = a 2 + b + c. a. What is the y-intercept? b. What is the ais of symmetry? c. Use the formula = - 2a b to find b. d. What is the equation of the parabola? 4 y O
5 Practice Modeling With Quadratic Functions Find an equation in standard form of the parabola passing through the points. 1. (1, -1), (2, -5), (3, -7) 2. (1, -4), (2, -3), (3, -4) 3. (2, -8), (3, -8), (6, 4) 4. (-1, -12), (2, -6), (4, -12) 5. (-1, -12), (0, -6), (3, 0) 6. (-2, -4), (1, -1), (3, 11) 7. (-1, -6), (0, 0), (2, 6) 8. (-3, 2), (1, -6), (4, 9) 9. f() 10. f() f() 12. f() The table shows the number n of tickets to a school play sold t days after the tickets went on sale, for several days. a. Find a quadratic model for the data. b. Use the model to find the number of tickets sold on day 7. c. When was the greatest number of tickets sold? 14. The table gives the number of pairs of skis sold in a sporting goods store for several months last year. a. Find a quadratic model for the data, using January as month 1, February as month 2, and so on. b. Use the model to predict the number of pairs of skis sold in November. c. In what month were the fewest skis sold? Day, t Month, t Jan Mar May Number of Tickets Sold, n Number of Pairs of Skis Sold, s
6 Practice (continued) Modeling With Quadratic Functions Determine whether a quadratic model eists for each set of values. If so, write the model. 15. f (-1) = -7, f (1) = 1, f (3) = f (-1) = 13, f (0) = 6, f (2) = f (2) = 2, f (-4) = -1, f (-2) = f (2) = 6, f (0) = -4, f (-2) = a. Complete the table. It shows the sum of the counting numbers from 1 through n. Number, n Sum, s b. Write a quadratic model for the data. c. Predict the sum of the first 50 counting numbers. 20. On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of one bridge is in the shape of the parabola y = , where y is the height in feet of the cable above the roadway at the distance feet from a support tower. a. What is the closest the cable comes to the roadway? b. How far from the support tower does this occur? 21. The owner of a small motel has an unusual idea to increase revenue. The motel has 20 rooms. He advertises that each night will cost a base rate of $48 plus $8 times the number of empty rooms that night. For eample, if all rooms are occupied, he will have a total income of 20 * $48 = $960. But, if three rooms are empty, then his total income will be (20-3) * ($48 + $8 # 3) = 17 * $72 = $1224. a. Write a linear epression to show how many rooms are occupied if n rooms are empty. b. Write a linear epression to show the price paid in dollars per room if n rooms are empty. c. Multiply the epressions from parts (a) and (b) to obtain a quadratic model for the data. Write the result in standard form. d. What will the owner s total income be if 10 rooms are empty? e. What is the number of empty rooms that results in the maimum income for the owner?
7 Practice Solving Quadratic Equations Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution = = = = = = = = = 0 Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. 10. t 2 = k 2 = z = d 2-14 = y 2-16 = g 2-32 = a 2 = = n 2-54 = c 2 = = j 2 = 0 Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. 22. Find the side length of a square with an area of 196 ft Find the radius of a circle with an area of 100 in Find the side length of a square with an area of 50 cm 2.
8 Practice (continued) Solving Quadratic Equations 25. The square tarp you are raking leaves onto has an area of 150 ft 2. What is the side length of the tarp? Round your answer to the nearest tenth of a foot if necessary. 26. There is enough mulch to spread over a flower bed with an area of 85 m 2. What is the radius of the largest circular bed that can be covered by the mulch? Round your answer to the nearest tenth of a meter if necessary. Mental Math Tell how many solutions each equation has. 27. q 2-22 = m = b 2-12 = 12 Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth z = t = a = h2-12 = m2 + 5 = = Find the value of n such that the equation 2 - n = 0 has 24 and -24 as solutions. Find the value of for the square and triangle. If necessary, round to the nearest tenth in m Writing Eplain how the number of solutions for a quadratic equation relates to the graph of the function.
9 Practice Factoring to Solve Quadratic Equations Use the Zero-Product Property to solve each equation. 1. (y + 6)(y - 4) = 0 2. (3f + 2)( f - 5) = 0 3. (2-7)(4 + 10) = 0 4. (8t - 7)(3t + 5) = 0 5. d(d - 8) = m(2m + 9) = 0 Solve by factoring. 7. n 2 + 2n - 15 = 0 8. a 2-15a + 56 = 0 9. z 2-10z + 24 = = b 2 + 7b - 6 = p 2-9p - 2 = w 2 + w = s s = d 2 = 5d 16. 3j 2-20j = y y = r r = 8 Use the Zero-Product Property to solve each equation. Write your solutions as a set in roster form. 19. k 2-11k + 30 = = n n + 72 = The volume of a sandbo shaped like a rectangular prism is 48 ft 3. The height of the sandbo is 2 feet. The width is w feet and the length is w + 2 feet. Use the formula V = lwh to find the value of w. 23. The area of the rubber coating for a flat roof was 96 ft 2. The rectangular frame the carpenter built for the flat roof has dimensions such that the length is 4 feet longer than the width. What are the dimensions of the frame? 24. Ling is cutting carpet for a rectangular room. The area of the room is 324 ft 2. The length of the room is 3 feet longer than twice the width. What should the dimensions of the carpet be?
10 Practice (continued) Factoring to Solve Quadratic Equations Write each equation in standard form. Then solve = n 2-2n + 1 = -3n 2 + 9n + 11 Find the value of as it relates to each rectangle or triangle. 27. Area = 60 cm Area = 234 yd Area = 20 in Area = 150 m Reasoning For each equation, find k and the value of any missing solutions k - 16 = 0 where -2 is one solution of the equation = k where 10 is one solution of the equation. 33. k 2-13 = 5 where is one solution of the equation. 34. Writing Eplain how you solve a quadratic equation by factoring.
11 Practice Completing the Square Find the value of c such that each epression is a perfect-square trinomial c 2. b b + c 3. g 2-20g + c 4. a 2-7a + c 5. w w + c 6. n 2-9n + c Solve each equation by completing the square. If necessary, round to the nearest hundredth. 7. z 2-19z = p 2-5p = b 2 + 6b = c 2-4c = a 2-2a = v 2 + 8v = y y = = h 2 + 4h = r 2 + 8r + 13 = d 2-2d - 4 = m 2-24m + 44 = 0 Solve each equation by completing the square. If necessary, round to the nearest hundredth y 2 + 5y = h 2-5h = k 2 + 4k = c 2 + 7c + 3 = f 2-2f = = The rectangle shown at the right has an area of 56 m 2. What is the value of? 3 1 2
12 Practice (continued) Completing the Square 26. What are all of the values of c that will make 2 + c + 49 a perfect square? 27. What are all of the values of c that will make 2 + c a perfect square? Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 28. k 2-24k + 4 = = b b + 15 = p 2 + 3p + 2 = m m - 80 = a 2-3a + 4 = a 2-12a + 28 = t 2-6t = Writing Discuss the strategies of graphing, factoring, and completing the square for solving the quadratic equation = The height of a triangle is 4 inches and the base is (5 + 1) inches. The area of the triangle is 500 square inches. What are the dimensions of the base and height of the triangle? 38. The formula for finding the volume of a rectangular prism is V = lwh. The height h of a rectangular prism is 12 centimeters. The prism has a volume of 10,800 cubic centimeters. The prism s length l is modeled by 3 centimeters and its width w by (2 + 1) centimeters. What is the value of? What are the dimensions of the length and the width? 39. Writing In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the square?
13 Practice The Quadratic Formula and the Discriminant Use the quadratic formula to solve each equation. 1. 7c 2 + 8c + 1 = w 2-28w = j 2-3j = = n 2-6n = d 2 + 2d + 9 = a 2 + 4a - 6 = p p = d 2-8d + 3 = 0 Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. 10. h 2-2h - 2 = = z 2-4z = t t = n n = s 2-10s + 14 = A basketball is passed through the air. The height h of the ball in feet after the distance d in feet the ball travels horizontally is given by h = -d d + 5. How far horizontally from the player passing the ball will the ball land on the ground? Which method(s) would you choose to solve each equation? Justify your reasoning. 17. h 2 + 4h + 7 = a 2-4a - 12 = y 2-11y - 14 = p 2-7p - 4 = = f 2-2f - 35 = Writing Eplain how the discriminant can be used to determine the number of solutions a quadratic equation has.
14 Practice (continued) The Quadratic Formula and the Discriminant Find the number of real-number solutions of each equation = = = = = = 0 Use any method to solve each equation. If necessary, round answers to the nearest hundredth m 2-3m - 15 = y 2 + 6y = a 2 = t 2-96 = z 2 + 7z = g 2 + 4g + 3 = 0 Find the value of the discriminant and the number of real-number solutions of each equation = = = = = = The weekly profit of a company is modeled by the function w = -g g The weekly profit, w, is dependent on the number of gizmos, g, sold. If the break-even point is when w = 0, how many gizmos must the company sell each week in order to break even? 43. Reasoning The equation b + 9 = 0 has no real-number solutions. What must be true about b? 44. Open-Ended Describe three different methods to solve = 0. Tell which method you prefer. Eplain your reasoning.
15 Practice Comple Numbers Simplify each number by using the imaginary number i Plot each comple number and find its absolute value i i i Simplify each epression. 10. (-2 + 3i) + (5-2i) 11. (-6 + 7i) + (6-7i) 12. (4-2i) - (-1 + 3i) 13. (-5 + 3i) - (-8 + 2i) 14. (4-3i)(-5 + 4i) 15. (2 - i)(-3 + 6i) 16. (5-3i)(5 + 3i) 17. (-1 + 3i) (4 - i) (-2i)(5i)(-i) i(2 + 2i) 25. 2(3-7i) - i(-4 + 5i)
16 Practice (continued) Comple Numbers Write each quotient as a comple number i 4i i 4-3i i i 7 5-2i Solve each equation. Check your answer = 49 Find all solutions to each quadratic equation = = = = = = a. Name the comple number represented by each point on the graph at the right. b. Find the additive inverse of each number. c. Find the comple conjugate of each number. d. Find the absolute value of each number. B 4 2 C 4i 2i 2i 4i Imaginary ais A Real ais 2 4 D
Quadratic Graphs and Their Properties
- Think About a Plan Quadratic Graphs and Their Properties Physics In a physics class demonstration, a ball is dropped from the roof of a building, feet above the ground. The height h (in feet) of the
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 informationThe Quadratic Formula
- The Quadratic Formula Content Standard Reviews A.REI..b Solve quadratic equations by... the quadratic formula... Objectives To solve quadratic equations using the Quadratic Formula To determine the number
More informationCHAPTER 8 Quadratic Equations, Functions, and Inequalities
CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.
More informationThe x-coordinate of the vertex: The equation of the axis of symmetry:
Algebra 2 Notes Section 4.1: Graph Quadratic Functions in Standard Form Objective(s): Vocabulary: I. Quadratic Function: II. Standard Form: III. Parabola: IV. Parent Function for Quadratic Functions: Vertex
More informationCHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING
CHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING Big IDEAS: 1) Graphing and writing quadratic functions in several forms ) Solving quadratic equations using a variety of methods 3) Performing operations with
More informationMATH 111 Departmental Midterm Exam Review Exam date: Tuesday, March 1 st. Exam will cover sections and will be NON-CALCULATOR EXAM.
MATH Departmental Midterm Eam Review Eam date: Tuesday, March st Eam will cover sections -9 + - and will be NON-CALCULATOR EXAM Terms to know: quadratic function, ais of symmetry, verte, minimum/maimum
More informationAlgebra 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 information5. Determine the discriminant for each and describe the nature of the roots.
4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
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 informationMini-Lecture 8.1 Solving Quadratic Equations by Completing the Square
Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.
More informationAlgebra 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 informationWrite each expression in terms of i : Add: (3 4i) (5 7i) (3 5) ( 4 7)i. 8 3i. Subtract: (3 4i) (5 7i) (3 4i) ( 5 7i) Find each product:
7_Ch09_online 7// 0:7 AM Page 9-0 9-0 CHAPTER 9 Quadratic Equations SECTION 9. Comple Numbers DEFINITIONS AND CONCEPTS EXAMPLES The imaginar number i is defined as Write each epression in terms of i :
More informationAdditional Factoring Examples:
Honors Algebra -3 Solving Quadratic Equations by Graphing and Factoring Learning Targets 1. I can solve quadratic equations by graphing. I can solve quadratic equations by factoring 3. I can write a quadratic
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,
More informationLesson 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 informationExam 2 Review F15 O Brien. Exam 2 Review:
Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to
More informationGraph Quadratic Functions in Standard Form
TEKS 4. 2A.4.A, 2A.4.B, 2A.6.B, 2A.8.A Graph Quadratic Functions in Standard Form Before You graphed linear functions. Now You will graph quadratic functions. Wh? So ou can model sports revenue, as in
More informationName Class Date. Quadratic Functions and Transformations. 4 6 x
- Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O
More informationCharacteristics 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 informationAlgebra 2 Unit 2 Practice
Algebra Unit Practice LESSON 7-1 1. Consider a rectangle that has a perimeter of 80 cm. a. Write a function A(l) that represents the area of the rectangle with length l.. A rectangle has a perimeter of
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 informationx (vertex is halfway between the x-intercepts)
Big Idea: A quadratic equation in the form a b c 0 has a related function f ( ) a b c. The zeros of the function are the -intercepts of its graph. These -values are the solutions or roots of the related
More informationMATH 110: FINAL EXAM REVIEW
MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set
More information4-1 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 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 informationProperties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a
0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value
More informationMA Review Worksheet for Exam 1, Summer 2016
MA 15800 Review Worksheet for Eam 1, Summer 016 1) Choose which of the following relations represent functions and give the domain and/or range. a) {(,5), (,5), ( 1,5)} b) equation: y 4 1 y 4 (5, ) 1 (
More informationMath 112 Spring 2018 Midterm 2 Review Problems Page 1
Math Spring 08 Midterm Review Problems Page Note: Certain eam questions have been more challenging for students. Questions marked (***) are similar to those challenging eam questions. Let f and g. (***)
More informationReady 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 information3 2 (C) 1 (D) 2 (E) 2. Math 112 Fall 2017 Midterm 2 Review Problems Page 1. Let. . Use these functions to answer the next two questions.
Math Fall 07 Midterm Review Problems Page Let f and g. Evaluate and simplify f g. Use these functions to answer the net two questions.. (B) (E) None of these f g. Evaluate and simplify. (B) (E). Consider
More informationGraph is a parabola that opens up if a 7 0 and opens down if a 6 0. a - 2a, fa - b. 2a bb
238 CHAPTER 3 Polynomial and Rational Functions Chapter Review Things to Know Quadratic function (pp. 150 157) f12 = a 2 + b + c Graph is a parabola that opens up if a 7 0 and opens down if a 6 0. Verte:
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 informationUnit 7 Quadratic Functions
Algebra I Revised 11/16 Unit 7 Quadratic Functions Name: 1 CONTENTS 9.1 Graphing Quadratic Functions 9.2 Solving Quadratic Equations by Graphing 9.1 9.2 Assessment 8.6 Solving x^2+bx+c=0 8.7 Solving ax^2+bx+c=0
More informationSECTION 3.1: Quadratic Functions
SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or
More informationSolving and Graphing Polynomials
UNIT 9 Solving and Graphing Polynomials You can see laminar and turbulent fl ow in a fountain. Copyright 009, K1 Inc. All rights reserved. This material may not be reproduced in whole or in part, including
More informationFinding Complex Solutions of Quadratic Equations
COMMON CORE y - 0 y - - 0 - Locker LESSON 3.3 Finding Comple Solutions of Quadratic Equations Name Class Date 3.3 Finding Comple Solutions of Quadratic Equations Essential Question: How can you find the
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 informationEquations and Inequalities
Equations and Inequalities Figure 1 CHAPTER OUTLINE.1 The Rectangular Coordinate Systems and Graphs. Linear Equations in One Variable.3 Models and Applications. Comple Numbers.5 Quadratic Equations.6 Other
More informationPAP Algebra 2. Unit 4B. Quadratics (Part 2) Name Period
PAP Algebra Unit 4B Quadratics (Part ) Name Period 1 After Test WS: 4.6 Solve by Factoring PAP Algebra Name Factor. 1. x + 6x + 8. 4x 8x 3 + + 3. x + 7x + 5 4. x 3x 1 + + 5. x + 7x + 6 6. 3x + 10x + 3
More informationMath Analysis Chapter 2 Notes: Polynomial and Rational Functions
Math Analysis Chapter Notes: Polynomial and Rational Functions Day 13: Section -1 Comple Numbers; Sections - Quadratic Functions -1: Comple Numbers After completing section -1 you should be able to do
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 2 Stud Guide-Chapters 8 and 9 Name Date: Time: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all square roots of the number. ) 600 9,
More informationProperties of Graphs of Quadratic Functions
Properties of Graphs of Quadratic Functions y = ax 2 + bx + c 1) For a quadratic function given in standard form a tells us: c is the: 2) Given the equation, state the y-intercept and circle the direction
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 2 27? 1. (7.2) What is the value of (A) 1 9 (B) 1 3 (C) 9 (D) 3
014-015 SEMESTER EXAMS SEMESTER 1. (7.) What is the value of 1 3 7? (A) 1 9 (B) 1 3 (C) 9 (D) 3. (7.3) The graph shows an eponential function. What is the equation of the function? (A) y 3 (B) y 3 (C)
More informationPractice Problems for Test II
Math 117 Practice Problems for Test II 1. Let f() = 1/( + 1) 2, and let g() = 1 + 4 3. (a) Calculate (b) Calculate f ( h) f ( ) h g ( z k) g( z) k. Simplify your answer as much as possible. Simplify your
More informationMath 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name
Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 Name Find the function value, provided it eists. 1) f() = 7-8 8 ; f(-3) Simplify by removing a factor equal to 1. ) 5 + 0 + 3) m - m - m Find
More informationBaruch College MTH 1030 Sample Final B Form 0809 PAGE 1
Baruch College MTH 00 Sample Final B Form 0809 PAGE MTH 00 SAMPLE FINAL B BARUCH COLLEGE DEPARTMENT OF MATHEMATICS SPRING 00 PART I (NO PARTIAL CREDIT, NO CALCULATORS ALLOWED). ON THE FINAL EXAM, THERE
More informationCompleting the Square
3.5 Completing the Square Essential Question How can you complete the square for a quadratic epression? Using Algera Tiles to Complete the Square Work with a partner. Use algera tiles to complete the square
More informationMAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam
MAT 33C -- Martin-Ga Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationFinal Exam Review Part 2 #1 Page 1 / 21
Final Eam Review Part #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: v 1. Solve for, where is a real number. v v + 1 + =. Solve for, where is a real number. +
More informationName: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown.
SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown. 1. What is the -ais measuring?. What is the y-ais measuring? 3. What are the
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 informationQuadratic Word Problems - Develop an Approach and Solve
Name: Class: Date: ID: A Quadratic Word Problems - Develop an Approach and Solve Short Answer 1. Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A = 7x x, where x = width,
More informationVisit us at: for a wealth of information about college mathematics placement testing!
North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics
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 informationSolve 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 informationThe point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, 2) B) (8, 2) C) ( 2, 8) D) (2, 8) E) ( 2, 8)
Name: Date: 1. Find the coordinates of the point. The point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, ) B) (8, ) C) (, 8) D) (, 8) E) (, 8). Find the coordinates
More informationSection 7.1 Objective 1: Solve Quadratic Equations Using the Square Root Property Video Length 12:12
Section 7.1 Video Guide Solving Quadratic Equations by Completing the Square Objectives: 1. Solve Quadratic Equations Using the Square Root Property. Complete the Square in One Variable 3. Solve Quadratic
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 information5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add
Chapter : Quadratic Equations and Functions Chapter Review Eercises... 5 8 6 8 The solution set is 8, 8. 5 5 5 5 5 5 The solution set is 5,5. Rationalize the denominator. 6 The solution set is. 8 8 9 6
More information1.5. Solve Quadratic Equations. Investigate
1.5 Solve Quadratic Equations Aleandre Despatie is a Canadian diver who has won two Olympic silver medals. One of the keys to a successful dive is for Aleandre to jump upward and outward to ensure that
More information10.7. Interpret the Discriminant. For Your Notebook. x5 2b 6 Ï} b 2 2 4ac E XAMPLE 1. Use the discriminant KEY CONCEPT
10.7 Interpret the Discriminant Before You used the quadratic formula. Now You will use the value of the discriminant. Wh? So ou can solve a problem about gmnastics, as in E. 49. Ke Vocabular discriminant
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 informationUNIT #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 informationChapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point.
Chapter : Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. f( ) 10, (, ) 10 1 E) none of the above. Find the slope of the tangent line to the
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 information16x y 8x. 16x 81. U n i t 3 P t 1 H o n o r s P a g e 1. Math 3 Unit 3 Day 1 - Factoring Review. I. Greatest Common Factor GCF.
P a g e 1 Math 3 Unit 3 Day 1 - Factoring Review I. Greatest Common Factor GCF Eamples: A. 3 6 B. 4 8 4 C. 16 y 8 II. Difference of Two Squares Draw ( - ) ( + ) Square Root 1 st and Last Term Eamples:
More informationMPM2D Trigonometry Review
MPM2D Trigonometry Review 1. What are the three primary trig ratios for each angle in the given right triangle? 2. What is cosθ? 3. For the following triangles, if ΔABC~ΔDFE, state a)the ratio of side
More informationWhich boxplot represents the same information as the histogram? Test Scores Test Scores
Frequency of Test Scores ALGEBRA I 01 013 SEMESTER EXAMS SEMESTER 1. Mrs. Johnson created this histogram of her 3 rd period students test scores. 8 6 4 50 60 70 80 90 100 Test Scores Which boplot represents
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 informationDate: Pd: Unit 4. GSE H Analytic Geometry EOC Review Name: Units Rewrite ( 12 3) 2 in simplest form. 2. Simplify
GSE H Analytic Geometry EOC Review Name: Units 4 7 Date: Pd: Unit 4 1. Rewrite ( 12 3) 2 in simplest form. 2. Simplify 18 25 3. Which expression is equivalent to 32 8? a) 2 2 27 4. Which expression is
More informationMath 150: Intermediate Algebra Spring 2012 Fall 2005 : Mock Exam 4 (z z
Math 150: Intermediate Algebra Spring 01 Fall 005 : Mock Eam 4 (z 9. - z NAME 10.6) TICKET # [ 13 problems: 10 points each ] Answer problems and epress your answers appropriately, that is ; simply state
More informationTEST 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 informationSection 7.1 Solving Quadratic Equations by Graphing. Solving Quadratic Equations by Graphing
Unit III Quadratic Equations 1 Section 7.1 Solving Quadratic Equations by Graphing Goal: Solving Quadratic Equations by Graphing Investigating Solutions to Quadratic Equations Eample: A missile fired from
More informationGet Ready. Scatter Plots 1. The scatter plot shows the height of a maple tree over a period of 7 years.
Get Ready BLM 4... Scatter Plots. The scatter plot shows the height of a maple tree over a period of 7 years. a) Identify the independent variable and the dependent variable. Describe the relationship
More informationPre-Calc Chapter 1 Sample Test. D) slope: 3 4
Pre-Calc Chapter 1 Sample Test 1. Use the graphs of f and g to evaluate the function. f( x) gx ( ) (f o g)(-0.5) 1 1 0 4. Plot the points and find the slope of the line passing through the pair of points.
More informationNonlinear Systems. No solution One solution Two solutions. Solve the system by graphing. Check your answer.
8-10 Nonlinear Sstems CC.9-1.A.REI.7 Solve a simple sstem consisting of a linear equation and a quadratic equation in two variables algebraicall and graphicall. Objective Solve sstems of equations in two
More informationINTERMEDIATE ALGEBRA REVIEW FOR TEST 3
INTERMEDIATE ALGEBRA REVIEW FOR TEST 3 Evaluate the epression. ) a) 73 (-4)2-44 d) 4-3 e) (-)0 f) -90 g) 23 2-4 h) (-2)4 80 i) (-2)5 (-2)-7 j) 5-6 k) 3-2 l) 5-2 Simplify the epression. Write your answer
More informationCalculus with the TI-89. Sample Activity: Exploration 7. Brendan Kelly
Calculus with the TI-89 Sample Activity: Eploration 7 Brendan Kelly EXPLORATION 7 Functions & Their Etrema Who Hit the Longest Home Run in Major League History? THE BETTMANN ARCHIVE Mickey Mantle 1931-1996
More information9.1 Practice A. Name Date sin θ = and cot θ = to sketch and label the triangle. Then evaluate. the other four trigonometric functions of θ.
.1 Practice A In Eercises 1 and, evaluate the si trigonometric functions of the angle. 1.. 8 1. Let be an acute angle of a right triangle. Use the two trigonometric functions 10 sin = and cot = to sketch
More informationAdvanced Algebra 2 Final Review Packet KG Page 1 of Find the slope of the line passing through (3, -1) and (6, 4).
Advanced Algebra Final Review Packet KG 0 Page of 8. Evaluate (7 ) 0 when and. 7 7. Solve the equation.. Solve the equation.. Solve the equation. 6. An awards dinner costs $ plus $ for each person making
More informationUnit 2. Quadratic Functions and Modeling. 24 Jordan School District
Unit Quadratic Functions and Modeling 4 Unit Cluster (F.F.4, F.F.5, F.F.6) Unit Cluster (F.F.7, F.F.9) Interpret functions that arise in applications in terms of a contet Analyzing functions using different
More information4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?
3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the
More informationThe Quadratic Formula VOCABULARY
- The Quadratic Formula TEKS FOCUS TEKS ()(F) Solve quadratic and square root equations. TEKS ()(G) Display, eplain, and justify mathematical ideas and arguments using precise mathematical language in
More informationREVIEW 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 informationUnit 3. Expressions and Equations. 118 Jordan School District
Unit 3 Epressions and Equations 118 Unit 3 Cluster 1 (A.SSE.): Interpret the Structure of Epressions Cluster 1: Interpret the structure of epressions 3.1. Recognize functions that are quadratic in nature
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 information7.4 Factored Form of a Quadratic
7. Factored Form of a Quadratic Function YOU WILL NEED graph paper and ruler OR graphing technology EXPLORE John has made a catapult to launch baseballs. John positions the catapult and then launches a
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 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 informationAdvanced Algebra Scope and Sequence First Semester. Second Semester
Last update: April 03 Advanced Algebra Scope and Sequence 03-4 First Semester Unit Name Unit : Review of Basic Concepts and Polynomials Unit : Rational and Radical Epressions Sections in Book 0308 SLOs
More information2 nd Semester Final Exam Review Block Date
Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. 1 (10-1) 1. (10-1). (10-1) 3. (10-1) 4. 3 Graph each function. Identif the verte, ais of smmetr, and
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 informationx 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12
Factor the GCF from each expression 4 5 1. 15x 3x. 16x 4 Name: a. b. 4 7 3 6 5 3. 18x y 36x y 4x y 5 4. 3x x 3 x 3 c. d. Not all may be possible. 1. Find two numbers that sum to 8 and have a product of
More informationChapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square
Chapter Notes Alg. H -A (Lesson -) Solving Quadratic Equations b Finding the Square Root and Completing the Square p. *Calculator Find the Square Root: take the square root of. E: Solve b finding square
More informationMath 20-1 Year End Review
M0- Year End Review.docx Name: Math 0- Year End Review hapter Sequences & Series... Pages hapter Trigonometr... Pages hapters & Quadratic Functions & Equations... Pages hapter Radicals... Pages hapter
More informationObjectives To solve quadratic equations using the quadratic formula To find the number of solutions of a quadratic equation
9-6 The Quadratic Formula and the Discriminant Content Standards A.REI..a Use the method of completing the square to transform an quadratic equation in into an equation of the form ( p) 5 q... Derive the
More information