MATH College Algebra Review for Test 2
|
|
- Hortense Fox
- 6 years ago
- Views:
Transcription
1 MATH 4 - College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of smmetr. (e) Graph f (x).. For f (x) = (x ) 8, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of smmetr. (e) Graph f (x).. The graph of the quadratic function f (x) is shown at the right. Determine the function's formula in the form f (x) = a(x h) + k. (,8) x 4. The graph of the quadratic function f (x) is shown at the right. Determine the function's formula in the form f ( x) = ax + bx + c x (, 8) 5. A baseball is hit so that its height s in feet after t seconds is given b s(t) = 5t + 40t + 5. (a) Find the maximum height of the baseball. (b) When does the baseball hit the ground? 6. Determine the zeros of the following quadratic functions and simplif our answers: (a) f ( x) = 4 x x + (b) f ( x) = x 6x + 7. Solve x 8x 4 = 0 b completing the square. Simplif our answer.
2 8. Determine the domain of f (x) = MATH 4 - College Algebra - Review for Test (Thomason) - p. of 8 x x. Give our answer in set-builder notation. x 0 9. For x 5x + = 0, (a) calculate the discriminant and (b) give the number of real solutions. Section. 0. For each of the following give our answer in a + bi form. (a) Add: ( + i) + ( 5 4i) (b) Subtract: ( 5 + 4i) ( i) (c) Multipl: ( i)( 4 + i) (d) Divide: 4 + i 5 i. Solve x = 6x 4 and simplif our answer. (Simplif radicals, reduce fractions, and express an imaginar numbers in terms of i.). How man real zeros does each of the following functions have? Section.4. The graph of f (x) = x x + is shown at the right. Solve f (x) 0 and give our answer in interval notation. (,4) (0,) (,0) (,0) 4. For the function f ( x) whose graph is show in Problem, for what values of x is f ( x) (a) increasing and (b) decreasing? Give our answers in interval notation.
3 MATH 4 - College Algebra - Review for Test (Thomason) - p. of 8 5. Solve the inequalit and write the solution set in interval notation: 7x 9x > 0 6. Solve the following inequalit and give our answer in interval notation: x + x Section.5 7. The graph of = f (x) is shown on the coordinate sstem at the right. Sketch the graphs of (a) = f (x + ), (b) = f ( x ) +, ( ), and (c) = f x (d) = f ( x). x 8. Let f (x) = x. Write a formula for a function g whose graph is similar to f (x) but is shifted right units and up 4 units. Section The graph of f (x) is shown on the coordinate sstem at the right. Determine the (a) local minima, (b) local maxima, (c) absolute minimum, (d) absolute maximum, (e) intervals in which f (x) is increasing, and (f) intervals in which f (x) is decreasing, if an. Give our answers to parts (e) and (f) in interval notation Determine whether each of the following is an even function, an odd function, or neither. Show or explain how ou determined our answer. (a) f (x) = x (b) f (x) = (x ) (c) f (x) = x + x. The table at the right is a complete representation of f. Is f an even function, an odd function, or neither? Show or explain how ou determined. x f(x)
4 Section 4.. Use the graph of the polnomial function f (x) shown at the right to answer the following. MATH 4 - College Algebra - Review for Test (Thomason) - p. 4 of 8 (a) How man turning points does the graph have? (b) Estimate the x-intercepts, assuming the are integers. x (c) Is the leading coefficient of f (x) positive or is it negative? (d) What is the minimum degree of f (x)?. For f ( x) = x + 5x +4x 5, (a) give the degree, (b) give the leading coefficient, (c) state the end behavior as x, and (d) state the end behavior as x. 4. For f ( x) = x 4 + x 8, (a) give the degree, (b) give the leading coefficient, (c) state the end behavior as x, and (d) state the end behavior as x. 5. Sketch a graph of a polnomial that satisfies the following conditions: Degree with two real zeros and a negative leading coefficient 6. Sketch a graph of a polnomial that satisfies the following conditions: Degree 4 with three real zeros and a negative leading coefficient 4 for x < 7. Let f ( x) = x for x x for x >. (a) Determine f ( ). (b) Determine f (). (c) Graph f ( x). (d) Give an values of x at which f ( x) is not continuous. Section Divide x 4x 0x b x Divide 6x x + 4 x 7 b x. 0. Is x + a factor of f (x) = x + 5x + x 6? Tell how ou determined our answer.. What is the remainder when x x + 4x 5 is divided b x?
5 Section 4.4 MATH 4 - College Algebra - Review for Test (Thomason) - p. 5 of 8. The graph of a rd, 4 th, or 5 th degree polnomial f (x) with integer zeros is shown at the right. Determine the factored form of f (x).. Solve exactl for x: 7x 5x x +5 = 0. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. 4. Solve exactl for x: x = 4x. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an complex solutions in standard form. 5. Solve exactl for x: x 6 =0x. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an complex solutions in standard form. 6. Find the zeros of f (x) = 7x + 5x +x 4 given that 7 is a zero. Section The graph of a 5 th degree polnomial f (x) is shown at the right. (a) How man different real zeros does f (x) have? (b) How man different imaginar zeros does f (x) have? x 8. Find the completel factored form of a polnomial f (x) with real coefficients that satisfies the following conditions: Degree ; a = ; zeros include and i
6 MATH 4 - College Algebra - Review for Test (Thomason) - p. 6 of 8 9. Find the completel factored form of a polnomial f (x) with real coefficients that satisfies the following conditions: Degree 4; a n = ; zeros include 0,, and i 40. (a) Find all the zeros of f ( x) = x x + 9x 7. (b) Write f (x) in completel factored form. 4. (a) Find all the zeros of f ( x) = 4x + x. (b) Write f (x) in completel factored form. 4. (a) Find all the zeros of f ( x) = x 4 6x +x. (b) Write f (x) in completel factored form. Section 4.7 (Polnomial Inequalities ) 4. Solve for x and give our solution in interval notation: x +5x < x 44. Solve for x and give our solution in interval notation: (x + 4)(x )(x 5) 0 Answers. (a) (,0), (5,0) (b) (0,5) (c) (,9) (d) x =. (a) (,0), (5,0) (b) (0,0) (c) (, 8) (d) x =
7 MATH 4 - College Algebra - Review for Test (Thomason) - p. 7 of 8. f ( x) = ( x +) f ( x) = x 4x 6 5. (a) ft (b) sec 6. (a) ± 5 (b) ± ± 5 8. { x x,5} 9. (a) (b) 0. (a) i (b) 8 + 6i (c) 0 +i (d) i 7 (a) x 7 (b) x. ± i. (a) (b) 0 (c). (, ] [, ) 4. (a) (, ] (b) [, ) 5. (,0) 9 7, 6. [ 4,] 7 (c) x 7 (d) x 8. g( x) = f (x ) + 4 = x (a) 0, 4 (b) (c) -4 (d) none (e) [, ], [, ) (f) (, ], [,] 0. (a) Even, because the graph is an open up parabola that is smmetric about the -axis. (b) Neither, because f ( x) = ( x ) = x + 6x + 9 but f ( x) = ( x ) = x 6x + 9 so f ( x) f ( x) and f ( x) f (x). (c) Neither, because f ( x) = ( x) + ( x) = x x but f ( x) = x + x so f ( x) f ( x) and f ( x) f (x).. Even, because f ( x) = f ( x) for all values of x in the domain of f.. (a) (b),, (c) positive (d) 4th
8 MATH 4 - College Algebra - Review for Test (Thomason) - p. 8 of 8. (a) rd (b) (c) f ( x) (d) f ( x) 4. (a) 4th (b) (c) f ( x) (d) f ( x) 5. Answers ma var. 6. Answers ma var. 7. (a) 4 (b) 9 8. x 7x + 6 x + 9. x + x + x (c) 0. Yes, because the remainder given b f () or division is 0.. (d). f ( x) = ( x +) (x )(x 4). ±, ± i 5., , ± 7 i 7. (a) (b) 8. f ( x) = (x )[x ( i)][x (+ i)] 9. f ( x) = x( x )(x i)( x + i) 40. (a), ±i (b) f ( x) = ( x )(x i)( x + i) 4. (a) 0, ±i (b) f ( x) = 4x( x i )(x + i ) ( ) ( ) 4. (a) 0, ± i (b) f ( x) = x x i x + i 4. (,0) (5, ) 44. [ 4,] {5}
MATH College Algebra Review for Test 2
MATH 34 - College Algebra Review for Test 2 Sections 3. and 3.2. For f (x) = x 2 + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the
More informationGraph the linear system and estimate the solution. Then check the solution algebraically.
(Chapters and ) A. Linear Sstems (pp. 6 0). Solve a Sstem b Graphing Vocabular Solution For a sstem of linear equations in two variables, an ordered pair (x, ) that satisfies each equation. Consistent
More informationAlgebra II Practice Semester Exam Specification Sheet
Algebra II Practice Semester Exam Specification Sheet 1. Properties of real numbers. Procedure (write procedure or process) 3. Concept development/linkage. Theorem/factual knowledge (of theorems and rules)
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 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 informationFINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name
FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name 1) Find the SUM of the solutions of the equation. 82 + 0 = 16 Use the quadratic formula to solve the equation. (All solutions are real numbers.)
More information1) The line has a slope of ) The line passes through (2, 11) and. 6) r(x) = x + 4. From memory match each equation with its graph.
Review Test 2 Math 1314 Name Write an equation of the line satisfying the given conditions. Write the answer in standard form. 1) The line has a slope of - 2 7 and contains the point (3, 1). Use the point-slope
More informationRF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?
RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct
More informationLearning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1
College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,
More informationAlgebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.
Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph
More information3 Polynomial and Rational Functions
3 Polnomial and Rational Functions 3.1 Quadratic Functions and Models 3.2 Polnomial Functions and Their Graphs 3.3 Dividing Polnomials 3.4 Real Zeros of Polnomials 3.5 Comple Zeros and the Fundamental
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 informationa [A] +Algebra 2/Trig Final Exam Review Fall Semester x [E] None of these [C] 512 [A] [B] 1) Simplify: [D] x z [E] None of these 2) Simplify: [A]
) Simplif: z z z 6 6 z 6 z 6 ) Simplif: 9 9 0 ) Simplif: a a a 0 a a ) Simplif: 0 0 ) Simplif: 9 9 6) Evaluate: / 6 6 6 ) Rationalize: ) Rationalize: 6 6 0 6 9) Which of the following are polnomials? None
More informationUnit 2 Notes Packet on Quadratic Functions and Factoring
Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a
More informationAPPLIED ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY
APPLIED ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Constructed Response # Objective Sllabus Objective NV State Standard 1 Graph a polnomial function. 1.1.7.1 Analze graphs of polnomial functions
More informationMath Intermediate Algebra
Math 095 - Intermediate Algebra Final Eam Review Objective 1: Determine whether a relation is a function. Given a graphical, tabular, or algebraic representation for a function, evaluate the function and
More information1 Quadratic Functions
Unit 1 Quadratic Functions Lecture Notes Introductory Algebra Page 1 of 8 1 Quadratic Functions In this unit we will learn many of the algebraic techniques used to work with the quadratic function fx)
More informationMATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)
MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the
More informationBRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH 05 Review Sheet
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH 05 Review Sheet Go to http://www.cun.edu/testing for more information on the CUNY Elementar Algebra
More informationMATH 0312 FINAL EXAM REVIEW ITEMS
MATH 012 FINAL EXAM REVIEW ITEMS Name The items on this review are representative of the items that ou might see on our course final eam. No formul sheets are allowed and calculators are not allowed on
More informationChapter 5 Smartboard Notes
Name Chapter 5 Smartboard Notes 10.1 Graph ax 2 + c Learning Outcome To graph simple quadratic functions Quadratic function A non linear function that can be written in the standard form y = ax 2 + bx
More information2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
More informationCollege Algebra ~ Review for Test 2 Sections
College Algebra ~ Review for Test Sections. -. Use the given graphs of = a + b to solve the inequalit. Write the solution set in interval notation. ) - + 9 8 7 6 (, ) - - - - 6 7 8 - Solve the inequalit
More informationCumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Cumulative Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the algebraic expression for the given value or values of the variable(s).
More informationLesson 9 Exploring Graphs of Quadratic Functions
Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point
More informationFirst Semester Final Review NON-Graphing Calculator
Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through
More informationMATH 2 TEST FORM B. 1. Which equation has exactly one real solution? a. 4x 2 12x 9 = 0 b. 4x x + 9 = 0 c. 4x 2 6x 9 = 0 d.
MATH TEST FORM B Name: 1. Which equation has exactl one real solution? a. 4x 1x 9 = 0 b. 4x + 1x + 9 = 0 c. 4x 6x 9 = 0 d. 4x + 6x + 9 = 0. Congruent squares, with side lengths of x, are cut from the corners
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 informationFinal Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i
Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add
More informationQuadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.
Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to
More informationMATH 115: Review for Chapter 6
MATH 115: Review for Chapter 6 In order to prepare for our test on Chapter 6, ou need to understand and be able to work problems involving the following topics: I SYSTEMS OF LINEAR EQUATIONS CONTAINING
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 informationSection 5.4 Quadratic Functions
Math 150 c Lynch 1 of 6 Section 5.4 Quadratic Functions Definition. A quadratic function is one that can be written in the form, f(x) = ax 2 + bx + c, where a, b, and c are real numbers and a 0. This if
More informationf(x) = 2x 2 + 2x - 4
4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms
More information(2.5) 1. Solve the following compound inequality and graph the solution set.
Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.
More informationMAT116 Final Review Session Chapter 3: Polynomial and Rational Functions
MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form f x = ax 2 + bx + c,
More informationGraphing Calculator Computations 2
Graphing Calculator Computations A) Write the graphing calculator notation and B) Evaluate each epression. 4 1) 15 43 8 e) 15 - -4 * 3^ + 8 ^ 4/ - 1) ) 5 ) 8 3 3) 3 4 1 8 3) 7 9 4) 1 3 5 4) 5) 5 5) 6)
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 informationMAC College Algebra
MAC 05 - College Algebra Name Review for Test 2 - Chapter 2 Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact distance between the
More informationRoots are: Solving Quadratics. Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3. real, rational. real, rational. real, rational, equal
Solving Quadratics Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3 Roots are: real, rational real, rational real, rational, equal real, irrational 1 To find the roots algebraically, make
More informationMth Quadratic functions and quadratic equations
Mth 0 - Quadratic functions and quadratic equations Name Find the product. 1) 8a3(2a3 + 2 + 12a) 2) ( + 4)( + 6) 3) (3p - 1)(9p2 + 3p + 1) 4) (32 + 4-4)(2-3 + 3) ) (4a - 7)2 Factor completel. 6) 92-4 7)
More informationName Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!
Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).
More informationCollege Algebra Final, 7/2/10
NAME College Algebra Final, 7//10 1. Factor the polnomial p() = 3 5 13 4 + 13 3 + 9 16 + 4 completel, then sketch a graph of it. Make sure to plot the - and -intercepts. (10 points) Solution: B the rational
More informationMth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula
Mth 95 Module 4 Chapter 8 Spring 04 Review - Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b
More informationEam Name algebra final eam review147 aam032020181t4highschool www.alvarezmathhelp.com MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation.
More informationPolynomial and Rational Functions
Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define
More informationChapter 2: Polynomial and Rational Functions
Chapter 2: Polynomial and Rational Functions Section 2.1 Quadratic Functions Date: Example 1: Sketching the Graph of a Quadratic Function a) Graph f(x) = 3 1 x 2 and g(x) = x 2 on the same coordinate plane.
More informationIntermediate Algebra Math 097. Evaluates/Practice Tests. For solutions, refer to the back of the PAN.
Intermediate Algebra Math 097 Evaluates/Practice Tests For solutions, refer to the back of the PAN. Page of 8 Take this practice test to be sure that ou are prepared for the final quiz in Evaluate.. Solve
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationMath 95 Practice Final Exam
Part 1: No Calculator Evaluating Functions and Determining their Domain and Range The domain of a function is the set of all possible inputs, which are typically x-values. The range of a function is the
More information( ), slope = 4 ( ) ( ) ( ) ( ) ( ) 2 x 1 ) y = 4( x 1) PreCalculus Basics Homework Answer Key. 4-1 Free Response. 9. ( 3, 0) parallel to 4x 3y = 0
PreCalculus Basics Homework Answer Ke 4-1 Free Response 1. ( 1, 1), slope = 1 2 3. 1, 0 +1= 1 ( 2 x 1 ), slope = 4 0 = 4( x 1) = 4( x 1) 5. ( 1, 1) and ( 3, 5) m = 5 1 3 1 = 2 1 = 2 x 1 or 5 = 2 x 3 7.
More informationCHAPTER 2 Polynomial and Rational Functions
CHAPTER Polnomial and Rational Functions Section. Quadratic Functions..................... 9 Section. Polnomial Functions of Higher Degree.......... Section. Real Zeros of Polnomial Functions............
More information4. exponential decay; 20% 9.1 Practice A found square root instead of cube root 16 =
9.. eponential deca; 0% 9. Practice A.. 7. 7.. 6. 9. 0 7.. 9. 0. found square root instead of cube root 6 = = = 9. = 7, 9. =,.. 7n 7n. 96. =, 97. =, 9. linear function: = + 0 99. quadratic function: =
More informationTest # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name
Test # Review Sections (.,.,., & ch. 3) Math 131 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the equation of the line. 1) -intercept,
More informationFor questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)
Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions -, insert , or = to make the sentence true. (1pt each) A. 5
More informationSolving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
More informationFinal Exam Review for DMAT 0310
Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x
More information, a 1. , a 2. ,..., a n
CHAPTER Points to Remember :. Let x be a variable, n be a positive integer and a 0, a, a,..., a n be constants. Then n f ( x) a x a x... a x a, is called a polynomial in variable x. n n n 0 POLNOMIALS.
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 informationmath FALL developmental mathematics sullivan 1e
TSIpractice eam review 1 131 180 plus 34 TSI questions for elementar and intermediate algebra m0300004301 aaa Name www.alvarezmathhelp.com math0300004301 FALL 01 100 interactmath developmental mathematics
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationC) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution
Sample Departmental Final - Math 46 Perform the indicated operation. Simplif if possible. 1) 7 - - 2-2 + 3 2 - A) + - 2 B) - + 4-2 C) + 4-2 D) - + - 2 Solve the problem. 2) The sum of a number and its
More informationAdvanced Algebra II 1 st Semester Exam Review
dname Advanced Algebra II 1 st Semester Exam Review Chapter 1A: Number Sets & Solving Equations Name the sets of numbers to which each number belongs. 1. 34 2. 525 3. 0.875 4. Solve each equation. Check
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 information4.1 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 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 informationName Please print your name as it appears on the class roster.
Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes
More informationMath 100 Final Exam Review
Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know.
More information3 Inequalities Absolute Values Inequalities and Intervals... 4
Contents 1 Real Numbers, Exponents, and Radicals 2 1.1 Rationalizing the Denominator................................... 2 1.2 Factoring Polynomials........................................ 2 1.3 Algebraic
More informationChapter 8 ~ Quadratic Functions and Equations In this chapter you will study... You can use these skills...
Chapter 8 ~ Quadratic Functions and Equations In this chapter you will study... identifying and graphing quadratic functions transforming quadratic equations solving quadratic equations using factoring
More information2.1 Quadratic Functions
Date:.1 Quadratic Functions Precalculus Notes: Unit Polynomial Functions Objective: The student will sketch the graph of a quadratic equation. The student will write the equation of a quadratic function.
More informationAlgebra I Final Exam Review 2016 List of Topics Covered
Algebra I Final Exam Review 016 List of Topics Covered Know all vocabular, pa attention to the highlighted words in the text, and understand the various tpes of directions in each of the sections 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 informationCheck boxes of Edited Copy of Sp Topics (was 217-pilot)
Check boxes of Edited Copy of 10024 Sp 11 213 Topics (was 217-pilot) College Algebra, 9th Ed. [open all close all] R-Basic Algebra Operations Section R.1 Integers and rational numbers Rational and irrational
More informationMath 0308 Final Exam Review(answers) Solve the given equations. 1. 3x 14 8x 1
Math 8 Final Eam Review(answers) Solve the given equations.. 8.. 9.. 9 9 8 8.. 8 8 all real numbers 8. 9. all real numbers no solution 8 8 9 9 9 Solve the following inequalities. Graph our solution on
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 informationChapter R - Basic Algebra Operations (94 topics, no due date)
Course Name: Math 00024 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 207 topics Textbook: Barnett/Ziegler/Byleen/Sobecki:
More informationTest # 33 QUESTIONS MATH131 091700 COLLEGE ALGEBRA Name atfm131bli www.alvarezmathhelp.com website MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More informationSolve the problem. Determine the center and radius of the circle. Use the given information about a circle to find its equation.
Math1314-TestReview2-Spring2016 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Is the point (-5, -3) on the circle defined
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 informationLaw of Sines, Law of Cosines, Heron s Formula:
PreAP Math Analsis nd Semester Review Law of Sines, Law of Cosines, Heron s Formula:. Determine how man solutions the triangle has and eplain our reasoning. (FIND YOUR FLOW CHART) a. A = 4, a = 4 ards,
More informationMath 100 Final Exam Review
Math 0 Final Eam Review Name The problems included in this review involve the important concepts covered this semester. Work in groups of 4. If our group gets stuck on a problem, let our instructor know.
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1 Final Eam Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) - - 6 = - + 7 1) ) 6 + 7(- - ) = -8 - ) ) - t + t = 6 t + 1 ) Solve
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 informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8
More information171S3.2 Quadratic Equations, Functions, Zeros, and Models September 30, Quadratic Equations, Functions, Zeros, and Models
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 3: Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and
More informationCHAPTER 3: Quadratic Functions and Equations; Inequalities
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 3: Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and
More informationy x+ 2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25 inches, find the width of the frame.
. Simplif the complex fraction x 4 4 x. x 4 x x 4 x x 4 x x 4 x x E) 4 x. A rectangular frame for a painting has a perimeter of 8 inches. If the length of the frame is inches, find the width of the frame.
More informationL What are the properties that should be used to isolate the variable in the equation? 3x + 11 = 5
lgebra Name: MITERM REVIEW Part Hour: ate: L... What are the properties that should be used to isolate the variable in the equation? x + = 5 additive identit and multiplicative identit additive inverse
More informationLocal Maximums and Local Minimums of Functions. f(x, y) has a local minimum at the point (x 0, y 0 ) if f(x 0, y 0 ) f(x, y) for
Local Extrema Previousl we have taken the partial derivative of a function f(x, ). But those partial derivatives were themselves functions and so we can take their partial derivatives. Local Maximums and
More informationPrecalculus Prerequisite Packet Paint Branch High School Math Department. Concepts To Be Assessed on the Precalculus Course Pre-assessment.
Updated /01 The problems in this packet are designed to help ou review topics from previous math courses that are important to our success in Precalculus. It is important that ou take time during summer
More informationreview math0410 (1-174) and math 0320 ( ) aafinm mg
Eam Name review math04 (1-174) and math 0320 (17-243) 03201700aafinm0424300 mg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif. 1) 7 2-3 A)
More informationReview for Midterm Exam
Algebra Name n ]0\sD tkkustsaf ASPoRfrtfwZaArHep clzldcg.q L maflnlp orbitgjhxtlsr LrmeesaecrbvFedk. Review for Midterm Eam Graph each line. Date ) = + ) + 5 = 0 5 5-5 - Find the inverse of the linearfunction.
More informationQUADRATIC GRAPHS ALGEBRA 2. Dr Adrian Jannetta MIMA CMath FRAS INU0114/514 (MATHS 1) Quadratic Graphs 1/ 16 Adrian Jannetta
QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape
More informationMath 115: Review for Chapter 2
Math 5: Review for Chapter Can ou determine algebraicall whether an equation is smmetric with respect to the - ais, the -ais, or the origin?. Algebraicall determine whether each equation below is smmetric
More information3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR
Name: Algebra Final Exam Review, Part 3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR. Solve each of the following equations. Show your steps and find all solutions. a. 3x + 5x = 0 b. x + 5x - 9 = x + c.
More informationChapter Five Notes N P U2C5
Chapter Five Notes N P UC5 Name Period Section 5.: Linear and Quadratic Functions with Modeling In every math class you have had since algebra you have worked with equations. Most of those equations have
More information