Lesson 8.2 Exercises, pages
|
|
- Everett Morris
- 5 years ago
- Views:
Transcription
1 Lesson 8. Eercises, pages 38 A Students should verif the solutions to all equations.. Which values of are not roots of each equation? a) ƒ - 3 ƒ = 7 = 5 or =- Use mental math. 5: L.S. 7 R.S. 7 : L.S. 7 R.S. 7 So, both 5 and are roots. b) ƒ - + ƒ = 8 =-0.5 or = 3 Use mental math. 0.5: L.S. 8 R.S. 8 3: L.S. R.S. 8 So, 3 is not a root of the equation. c) ƒ ƒ = 8 = or =-0.75 Use a calculator. : L.S. 8 R.S : L.S..815 R.S. 8 So, 0.75 is not a root of the equation. 5. Use the graphs to determine the approimate solutions of each equation. Where necessar, give the solutions to the nearest tenth. a) ƒ ƒ = 9 b) ƒ - ƒ = The line 9 intersects The line 1 intersects 3 3 at points: at points, (, 9) and (, 9). So, the which appear to be: solutions are and. ( 1.7, 1), ( 1, 1), (1, 1), and (1.7, 1). So, the solutions are 1.7, 1, 1, and Solving Absolute Value Equations Solutions DO NOT COPY. P
2 B. Solve b graphing. a) 5 = ƒ ƒ b) = ƒ 5 - ƒ To graph 1, To graph 5, graph graph 1, then 5, then reflect, in the reflect, in the -ais, the part -ais, the part of the graph that of the graph that is below the is below the -ais. The line -ais. The line 5 intersects does not intersect 1 at ( 1, 5) and 5. So, the (1.5, 5). So, the solutions are equation has no solution. 1 and 1.5. c) ƒ - 3 ƒ = 9 d) ƒ + 8 ƒ = To graph 3, To graph 8, graph graph 3, then 8, then reflect, in the reflect, in the -ais, the -ais, the part of the graph that part of the graph that is below the -ais. The line is below the -ais. 0 intersects 8 The line 9 intersects at (, 0). So, the solution is 3 at ( 3, 9). and (, 9). So, the solutions are 3 and. P DO NOT COPY. 8. Solving Absolute Value Equations Solutions 11
3 7. Solve b graphing. Where necessar, give the solutions to the nearest tenth. a) ƒ ƒ = b) = ƒ ƒ Enter 1 and Enter 3 and in the graphing calculator. in the graphing calculator. The line appears to The line appears to intersect intersect 1 at 3 at points: points: ( , ) and ( ,),( 1.5, ), (0, ), (.1..., ). and ( ,).So,the So, the equation has solutions: equation has solutions: 0. and...9, 1.5, 0, and 1.. c) = ƒ ƒ d) Enter 7 3 and in the graphing calculator. The line appears to intersect 7 3 at points: ( , ) and ( , ). So, the equation has solutions: 3.9 and 0.. ƒ ƒ = Enter and in the graphing calculator. The line does not intersect. So, the equation has no solution. 8. Use algebra to solve each equation. a) ƒ + 3 ƒ = 3 if 3» 0 that is, if» 3 When» 3 : » 3, so this root ( 3) if 3<0 that is, if < 3 When < 3 : ( 3) < 3, so this root The solutions are 1 and Solving Absolute Value Equations Solutions DO NOT COPY. P
4 b) 3 = ƒ + 5 ƒ 5 3 if 5» 0 that is, if» 5 ( 5) if 5<0 that is, if < 5 When» 5 : » 5, so this root The solutions are 1and. When < 5 : ( 5) < 5, so this root c) = ƒ ƒ When 5» 0: When 5<0: 5 ( 5) ( 1)( 3) or 3 _ () (1)(7) (1) _ 1 This is not a real number. So, 1and 3are the solutions. d) ƒ ƒ = 5 When 5» 0: When 5<0: 5 5 ( 5) 5 0 ( ) 0 0 or _ ( ) (1)(10) (1) _ This is not a real number. So, 0 and are the solutions. P DO NOT COPY. 8. Solving Absolute Value Equations Solutions 13
5 9. For which values of c does the equation ƒ 3 + ƒ = c have: a) solutions? This is the graph of 3. For the equation to have solutions, the line c must intersect the graph of 3 at points; that is, c> b) 1 solution? For the equation to have 1 solution, the line c must intersect the graph of 3 at 1 point; that is, c 0. c) no solution? For the equation to have no solution, the line c must not intersect the graph of 3 ; that is, c< A manufacturer rejects 75-g boes of crackers when the actual mass of the bo differs from the stated mass b more than 3.5 g. a) Write an absolute value equation that can be used to determine the greatest and least masses that are acceptable. Let m grams represent the mass of a bo of crackers. So, an equation is: m b) Solve the equation. What is the least mass that is acceptable? What is the greatest mass? When m 75» 0: When m 75<0: m (m 75) 3.5 m 78.5 m m 71.5 So, the least acceptable mass is 71.5 g and the greatest mass is 78.5 g Solving Absolute Value Equations Solutions DO NOT COPY. P
6 11. Use algebra to solve each equation. a) ƒ + 1 ƒ = (7 ) 1 1 (7 ) if 1» 0 that is, if» 1 ( 1) 1 (7 ) if 1<0 that is, if < 1 When» 1 : When < 1 : 1 1 (7 ) ( 1) 1 (7 ) » 1, so this root 9 < 1, so this root 5 The solutions are 5 and b) = ƒ - 11 ƒ When 11» 0: When 11<0: ( 11) ( 11)( 1) or 1 ( 11)( 1) 0 11 or 1 So, 1, 1, and 11 are the solutions. c) ` 1-3 ` = ( ) if » 0 if <0 that is, if» 1.5 that is, if <1.5 When» 1.5: When <1.5: ( ) » 1.5, so this root.5.5<1.5, so this root The solutions are.5 and 9.5. P DO NOT COPY. 8. Solving Absolute Value Equations Solutions 15
7 d) = ƒ + ƒ When» 0: When <0: 3 18 ( ) 3 18 ( ) ( )( 3) ( )( 3) 0 or 3 or 3 So,, 3, and 3 are the solutions. 1. A student solved the equation ƒ ƒ - = -3 and reasoned that since the absolute value of an epression cannot be negative, the equation has no solution. Is the student correct? Eplain. If the student is not correct, describe the error the student made and solve the equation. The student is incorrect. The student should have simplified the equation first b adding to both sides. Then the equation becomes Correct solution: ( 3 1) ( 1)( ) ( 3) 0 1 or 0 or 3 So,, 3, 0, and 1 are the solutions. 13. A car is travelling toward the British Columbia-Alberta border. The car is 150 km from the border and is travelling at an average speed of 100 km/h. a) Write an absolute value equation to represent the distance, d kilometres, of the car from the border after t hours. After 1 h, the car has travelled 100 km. After t hours, the car has travelled 100t kilometres. So, the distance from the border after t hours is represented b the equation: d t 1 8. Solving Absolute Value Equations Solutions DO NOT COPY. P
8 b) Determine when the car is 5 km from the border. Eplain our strateg. Substitute: d t When t» 0: When t<0: t 5 ( t) 100t t t t 175 t 1 3 So, the car is 5 km from the border after 1 1 h and after 1 3 h. The car can be 5 km from the border on the Alberta side or 5 km from the border on the British Columbia side. C 1. The function = f () is linear. The line = intersects = ƒ f () ƒ at = and = 0. The line = 3 intersects = ƒ f () ƒ at = 1 and = 3. What is an equation for the function = f ()? f() 0 f() passes through the points (0, ), (, ), (1, 3), and (3, 3). Plot the points. The points are smmetrical about the line, so plot a point at (, 0). Join the points from (, 0) to (0, ) and from (, 0) to (, ) with straight lines. An equation for the right branch of the graph has the form m b. m 3 3 m 3 Use: 3 b Substitute: and 3() b b So, an equation for the function f() is 3. P DO NOT COPY. 8. Solving Absolute Value Equations Solutions 17
9 15. A student used this graph to solve an absolute value equation. What might the equation have been? Eplain our strateg The line has -intercept 3 and -intercept 3. An equation of the line has the form m 3. Use the point ( 3, 0). Substitute: 3and 0 0 m( 3) 3 m 1 So, an equation of the line is: 3 Assume the middle piece of the graph was reflected in the -ais. So, the graph of the quadratic function opens up and has verte (0, 9). So, the equation has the form a 9. An -intercept of the graph is 3, so use the point (3, 0). Substitute 3 and 0. 0 a(3) 9 0 9a 9 a 1 An equation for the quadratic function is 9, and an equation for the absolute value function is 9. So, the student might have used the graph to solve the equation: Solving Absolute Value Equations Solutions DO NOT COPY. P
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 informationLesson 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 informationSYSTEMS OF THREE EQUATIONS
SYSTEMS OF THREE EQUATIONS 11.2.1 11.2.4 This section begins with students using technology to eplore graphing in three dimensions. By using strategies that they used for graphing in two dimensions, students
More informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More informationStudy Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14.
Study Guide and Intervention Quadratic Formula The Quadratic Formula can be used to solve any quadratic equation once it is written in the form a 2 + b + c = 0. Quadratic Formula The solutions of a 2 +
More informationName Date. Analyzing Graphs of Polynomial Functions For use with Exploration 2.7
Name Date.7 Analyzing Graphs of Polynomial Functions For use with Eploration.7 Essential Question How many turning points can the graph of a polynomial function have? 1 EXPLORATION: Approimating Turning
More informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationMaintaining 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 informationREVIEW, pages
REVIEW, pages 5 5.. Determine the value of each trigonometric ratio. Use eact values where possible; otherwise write the value to the nearest thousandth. a) tan (5 ) b) cos c) sec ( ) cos º cos ( ) cos
More informationChapters 8 & 9 Review for Final
Math 203 - Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for
More informationLESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More informationLesson 5.6 Exercises, pages
Lesson 5.6 Eercises, pages 05 0 A. Approimate the value of each logarithm, to the nearest thousanth. a) log 9 b) log 00 Use the change of base formula to change the base of the logarithms to base 0. log
More informationLESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II
LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS
More information2 variables. is the same value as the solution of. 1 variable. You can use similar reasoning to solve quadratic equations. Work with a partner.
9. b Graphing Essential Question How can ou use a graph to solve a quadratic equation in one variable? Based on what ou learned about the -intercepts of a graph in Section., it follows that the -intercept
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 9 Prerequisite Skills
Name: Date: Chapter 9 Prerequisite Skills BLM 9. Consider the function f() 3. a) Show that 3 is a factor of f(). If f() ( 3)g(), what is g()?. Factor each epression fully. a) 30g 4g 6fg 8g c) 6 5 d) 5
More informationThe 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 informationMath 20-1 Functions and Equations Multiple Choice Questions
Math 0- Functions and Equations Multiple Choice Questions 8 simplifies to: A. 9 B. 0 C. 90 ( )( ) simplifies to: A. B. C. 8 A. 9 B. C. simplifies to: The area of the shaded region below is: 0 0 A. B. 0
More informationFUNCTIONS. Prepared by: Ms Sonia Tan
FUNCTIONS FUNCTION A function is a pairing that assigns to each element of the set X eactly one element of the set Y. Using Diagrams X Y 1 a b 3 c 4 d X 1 3 4 Y a b c X Y 1 a b 3 c One to One Many to One
More informationGraphing Linear Functions The collection of all input values is called the of a function.
Math /7 NTES (9.3) Name Graphing Linear Functions The collection of all input values is called the of a function. The collection of all output values is called the of a function. Make a table for the function.
More informationVertex 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 informationIB 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 informationSection 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 information1. Given the function f (x) = x 2 3bx + (c + 2), determine the values of b and c such that f (1) = 0 and f (3) = 0.
Chapter Review IB Questions 1. Given the function f () = 3b + (c + ), determine the values of b and c such that f = 0 and f = 0. (Total 4 marks). Consider the function ƒ : 3 5 + k. (a) Write down ƒ ().
More information-5(1-5x) +5(-8x - 2) = -4x -8x. Name Date. 2. Find the product: x 3 x 2 x. 3. Solve the following equation for x.
Name Date CC Algebra 2 Period Units 1-5 Review Due Tuesday, January 3, 2017 Answer all of the following questions. The number of each question corresponds to the lesson in which it was covered. Copying
More informationFor problems 1 4, evaluate each expression, if possible. Write answers as integers or simplified fractions
/ MATH 05 TEST REVIEW SHEET TO THE STUDENT: This Review Sheet gives you an outline of the topics covered on Test as well as practice problems. Answers are at the end of the Review Sheet. I. EXPRESSIONS
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 informationSuggested Problems for Math 122
Suggested Problems for Math 22 Note: This file will grow as the semester evolves and more sections are added. CCA = Contemporary College Algebra, SIA = Shaum s Intermediate Algebra SIA(.) Rational Epressions
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. Identif the verte and ais of smmetr. 1 (10-1) 1. (10-1). 3 (10-) 3. 4 7 (10-) 4. 3 6 4 (10-1) 5. Predict
More informationMaintaining 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 information9-1. 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 informationMATH 115: Review for Chapter 5
MATH 5: Review for Chapter 5 Can you find the real zeros of a polynomial function and identify the behavior of the graph of the function at its zeros? For each polynomial function, identify the zeros of
More informationQuadratic 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 informationSolving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic
9. Solving Quadratic Equations b Graphing equation in one variable? How can ou use a graph to solve a quadratic Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is
More informationEssential Question: How can you solve equations involving variable exponents? Explore 1 Solving Exponential Equations Graphically
6 7 6 y 7 8 0 y 7 8 0 Locker LESSON 1 1 Using Graphs and Properties to Solve Equations with Eponents Common Core Math Standards The student is epected to: A-CED1 Create equations and inequalities in one
More informationG r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Exam Answer Key
G r a d e P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Eam Answer Key G r a d e P r e - C a l c u l u s M a t h e m a t i c s Final Practice Eam Answer Key Name: Student Number:
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 informationLesson 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 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 informationD: all real; R: y g (x) = 3 _ 2 x 2 5. g (x) = 5 x g (x) = - 4 x 2 7. g (x) = -4 x 2. Houghton Mifflin Harcourt Publishing Company.
AVOID COMMON ERRORS Watch for students who do not graph points on both sides of the verte of the parabola. Remind these students that a parabola is U-shaped and smmetric, and the can use that smmetr to
More informationLast modified Spring 2016
Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7-, solve the following applications.
More information5.2 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 information12x y (4) 2x y (4) 5x y is the same as
Name: Unit #6 Review Quadratic Algebra Date: 1. When 6 is multiplied b the result is 0 1 () 9 1 () 9 1 () 1 0. When is multiplied b the result is 10 6 1 () 7 1 () 7 () 10 6. Written without negative eponents
More informationLESSON #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 information150. a. Clear fractions in the following equation and write in. b. For the equation you wrote in part (a), compute. The Quadratic Formula
75 CHAPTER Quadratic Equations and Functions Preview Eercises Eercises 8 50 will help you prepare for the material covered in the net section. 8. a. Solve by factoring: 8 + - 0. b. The quadratic equation
More informationKEY Algebra: Unit 9 Quadratic Functions and Relations Class Notes 10-1
Name: KEY Date: Algebra: Unit 9 Quadratic Functions and Relations Class Notes 10-1 Anatomy of a parabola: 1. Use the graph of y 6 5shown below to identify each of the following: y 4 identify each of the
More informationAnswer the following questions using a fraction and a percent (round to the nearest tenth of a percent).
ALGEBRA 1 Ch 10 Closure Solving Comple Equations Name: Two-Way Tables: A simple random sample of adults in a metropolitan area was selected and a survey was administered to determine the relationship between
More informationFair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal
Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the
More informationFair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.
Name Date Chapter 9 Find the square root(s). Fair Game Review... 9. ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif 0. 8. Simplif. 9. Simplif 08. 0. Simplif 88. Copright
More informationA11.1 Areas under curves
Applications 11.1 Areas under curves A11.1 Areas under curves Before ou start You should be able to: calculate the value of given the value of in algebraic equations of curves calculate the area of a trapezium.
More informationG r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Midterm Practice Exam Answer Key
G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Midterm Practice Eam Answer Key G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s Midterm Practice Eam Answer Key Name:
More informationNorthwest High School s Algebra 2/Honors Algebra 2
Northwest High School s Algebra /Honors Algebra Summer Review Packet 0 DUE Frida, September, 0 Student Name This packet has been designed to help ou review various mathematical topics that will be necessar
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 informationLesson 3.1 Linear Equations and Arithmetic Sequences
Lesson 3.1 Linear Equations and Arithmetic Sequences 1. Find an eplicit formula for each recursivel defined arithmetic sequence. a. u 0 18.25 b. t 0 0 u n u n 1 4.75 where n 1 t n t n 1 100 where n 1 2.
More informationUNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS
Answer Ke Name: Date: UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS Part I Questions. For the quadratic function shown below, the coordinates of its verte are, (), 7 6,, 6 The verte is
More informationPre-Calculus Summer Packet
Pre-Calculus Summer Packet Name ALLEN PARK HIGH SCHOOL Summer Assessment Pre-Calculus Summer Packet For Students Entering Pre-Calculus Summer 05 This summer packet is intended to be completed by the FIRST
More information6. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given by
MATH 34 - College Algebra Review for Test 3 Section 4.6. Let f ( ) = 3 5 + 4. (a) What is the domain? (b) Give the -intercept(s), if an. (c) Give the -intercept(s), if an. (d) Give the equation(s) of the
More informationMath 030 Review for Final Exam Revised Fall 2010 RH/ DM 1
Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab
More information5.2 Solving Linear-Quadratic Systems
Name Class Date 5. Solving Linear-Quadratic Sstems Essential Question: How can ou solve a sstem composed of a linear equation in two variables and a quadratic equation in two variables? Resource Locker
More information9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON
CONDENSED LESSON 9.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations solve
More informationHCC-SE MATH DEPT. 1 Revised Fall 2008
FINAL EXAM REVIEW ITEMS Math : College Algebra Find the -intercepts and an -intercepts. ) f() = + 7-0 ) = Name ) Select the equation that describes the graph. Solve the equation and epress the solution
More information(a) Show that there is a root α of f (x) = 0 in the interval [1.2, 1.3]. (2)
. f() = 4 cosec 4 +, where is in radians. (a) Show that there is a root α of f () = 0 in the interval [.,.3]. Show that the equation f() = 0 can be written in the form = + sin 4 Use the iterative formula
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 information11.1 Inverses of Simple Quadratic and Cubic Functions
Locker LESSON 11.1 Inverses of Simple Quadratic and Cubic Functions Teas Math Standards The student is epected to: A..B Graph and write the inverse of a function using notation such as f (). Also A..A,
More informationPreCalculus Honors: Functions and Their Graphs. Unit Overview. Student Focus. Example. Semester 1, Unit 2: Activity 9. Resources: Online Resources:
Resources: SpringBoard- PreCalculus PreCalculus Honors: Functions and Their Graphs Semester 1, Unit 2: Activity 9 Unit Overview In this unit, students study polynomial and rational functions. They graph
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 informationLesson 7.6 Exercises, pages
Lesson 7.6 Exercises, pages 658 665 A. Write each expression as a single trigonometric ratio. a) sin (u u) b) sin u sin u c) sin u sin u d) cos u cos u sin U cos U e) sin u sin u f) sin u sin u sin U 5.
More informationMATHEMATICS LEVEL 2 TEST FORM B Continued
Mathematics Level Test Form B For each of the following problems, decide which is the BEST of the choices given. If the eact numerical value is not one of the choices, select the choice that best approimates
More informationMATHEMATICS LEVEL 2. MATHEMATICS LEVEL 2 Continued GO ON TO THE NEXT PAGE USE THIS SPACE FOR SCRATCHWORK. 1. If xy 0 and 3x = 0.
MATHEMATICS LEVEL For each of the following problems, decide which is the BEST of the choices given. If the eact numerical value is not one of the choices, select the choice that best approimates this
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 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 informationFactoring Polynomials
5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.D 2A.7.E Factoring Polnomials Essential Question How can ou factor a polnomial? Factoring Polnomials Work with a partner. Match each polnomial equation with
More informationMEP Practice Book ES1. (h) (l) Simplify each of the following, leaving your answer in index notation.
Indices MEP Practice Book ES. Inde Notation. Write in a form using indices: a) b) c) d) 7 7 7 7 7 7 e) f) g) 7 7 7 7 h) i) 7 7 7 7 7 j) k) l). Find the value of the following: a) 7 b) c) d) 8 e) 7 0 f)
More informationHonors Math 2 Unit 1 Test #2 Review 1
Honors Math Unit 1 Test # Review 1 Test Review & Study Guide Modeling with Quadratics Show ALL work for credit! Use etra paper, if needed. Factor Completely: 1. Factor 8 15. Factor 11 4 3. Factor 1 4.
More informationMath 026 Review Exercises for the Final Exam
Math 06 Review Eercises for the Final Eam The following are review eercises for the Math 06 final eam. These eercises are provided for you to practice or test yourself for readiness for the final eam.
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(c) Find the gradient of the graph of f(x) at the point where x = 1. (2) The graph of f(x) has a local maximum point, M, and a local minimum point, N.
Calculus Review Packet 1. Consider the function f() = 3 3 2 24 + 30. Write down f(0). Find f (). Find the gradient of the graph of f() at the point where = 1. The graph of f() has a local maimum point,
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 informationSummer Review For Students Entering Algebra 2
Summer Review For Students Entering Algebra Teachers and administrators at Tuscarora High School activel encourage parents and communit members to engage in children s learning. This Summer Review For
More informationPre-Calculus Module 4
Pre-Calculus Module 4 4 th Nine Weeks Table of Contents Precalculus Module 4 Unit 9 Rational Functions Rational Functions with Removable Discontinuities (1 5) End Behavior of Rational Functions (6) Rational
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 informationUNCORRECTED 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 informationPreCalculus. American Heritage Upper School Summer Math Packet
! PreCalculus American Heritage Upper School Summer Math Packet All Upper School American Heritage math students are required to complete a summer math packet. This packet is intended for all students
More information8.2 Graphing More Complicated Rational Functions
1 Locker LESSON 8. Graphing More Complicated Rational Functions PAGE 33 Name Class Date 8. Graphing More Complicated Rational Functions Essential Question: What features of the graph of a rational function
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 informationPrecalculus Summer Packet
Precalculus Summer Packet These problems are to be completed to the best of your ability by the first day of school You will be given the opportunity to ask questions about problems you found difficult
More informationMath 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint.
Math 11. Practice Questions Chapters and 3 Fall 01 1. Find the other endpoint of the line segment that has the given endpoint and midpoint. Endpoint ( 7, ), Midpoint (, ). Solution: Let (, ) denote the
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its
More information10.1 Inverses of Simple Quadratic and Cubic Functions
COMMON CORE Locker LESSON 0. Inverses of Simple Quadratic and Cubic Functions Name Class Date 0. Inverses of Simple Quadratic and Cubic Functions Essential Question: What functions are the inverses of
More informationAlgebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
More informationGraphs of Basic Polynomial Functions
Section 1 2A: Graphs of Basic Polynomial Functions The are nine Basic Functions that we learn to graph in this chapter. The pages that follow this page will show how several values can be put into the
More informationPrinciples of Math 12: Logarithms Practice Exam 1
Principles of Math 1: Logarithms Practice Eam 1 www.math1.com Principles of Math 1 - Logarithms Practice Eam Use this sheet to record your answers 1. 10. 19. 30.. 11. 0. 31. 3. 1.. 3. 4. NR 3. 3. 33. 5.
More informationAlgebra 2 Semester Exam Review
Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation
More informationCHAPTER 2. Polynomial Functions
CHAPTER Polynomial Functions.1 Graphing Polynomial Functions...9. Dividing Polynomials...5. Factoring Polynomials...1. Solving Polynomial Equations...7.5 The Fundamental Theorem of Algebra...5. Transformations
More informationMCF3MI Unit 3: Solving Quadratic Equations
MCF3MI Unit 3: Solving Quadratic Equations MCF3MI Unit 3: Solving Quadratic Equations Lesson 1 Date: Quadratic Functions vs. Quadratic Equations A Quadratic Function of the form f() = a 2 + b + c, where
More informationMA 22000, Lesson 2 Functions & Addition/Subtraction Polynomials Algebra section of text: Sections 3.5 and 5.2, Calculus section of text: Section R.
MA 000, Lesson Functions & Addition/Subtraction Polynomials Algebra section of tet: Sections.5 and 5., Calculus section of tet: Section R.1 Definition: A relation is any set of ordered pairs. The set of
More information* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!
AdvPreCal 1 st Semester Final Eam Review Name 1. Solve using interval notation: 7 8 * Circle these problems: -7, 7, 0-, 8, 6-66 No Calculator!. Solve and graph: 0. Solve using a number line and leave answer
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve
More informationMath 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