# Identify a pattern and find the next three numbers in the pattern. 5. 5(2s 2 1) 2 3(s 1 2); s 5 4

Save this PDF as:

Size: px
Start display at page:

Download "Identify a pattern and find the next three numbers in the pattern. 5. 5(2s 2 1) 2 3(s 1 2); s 5 4"

## Transcription

1 Chapter 1 Test Do ou know HOW? Identif a pattern and find the net three numbers in the pattern. 1. 5, 1, 3, 7, c. 6, 3, 16, 8, c Each term is more than the previous Each term is half of the previous term; 11, 15, 19 term;,, 1 3. What properties of real numbers are illustrated b each equation below? a (8) Commutative Propert of Addition b. 1 () 5 0 Inverse Propert of Addition c. (8 1 t) 5? 8 1? t Distributive Propert d. 7 8? Inverse Propert of Multiplication Evaluate the epression for the given value of the variable.. a (a 1 1); a (s 1) 3(s 1 ); s The epression models the dail cost in dollars of renting scuba gear from the water sports store. In the epression, represents the number of hours the scuba gear is used. What is the cost of renting scuba gear for a da when the gear is used for 3 hours? \$30 Solve each equation. 7. r 1 5 3r (t 1 1) Solve each equation for. State an restrictions on the variables. 9. t a a 3 5 t ; t u

2 Chapter 1 Test (continued) Write an equation and solve the problem. 11. Two buses leave Columbus, Ohio at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 8 mi/h. When will the be 618 mi apart? 6 h Solve each inequalit. Graph the solution. 1. n 1 1 \$ 7 n L a 1 5, 6a 1 1 a S Solve each compound inequalit. Graph the solutions #6 or 1 1 \$ 3 K or L 115. t 1, and t, 6 1 R t R Solve each equation. Check for etraneous solutions. 16. u u or u b 1 u 5 b b The weatherman announced that the temperature T over the net few weeks will be at least 68F and at most 788F. Write an absolute value inequalit for the temperature over the net few weeks.»t 71 K7 Do ou UNDERSTAND? 19. What is another name for the multiplicative inverse? reciprocal 0. Reasoning Eplain in words wh u u, has no solution. Answers ma var. Sample: Dividing both sides b gives R. The absolute value of an number must be nonnegative, so the inequalit has no solution. 1. Open-Ended What is the difference between simplifing an epression and evaluating an epression? Answers ma var. Sample: Simplifing an epression is rewriting it using the properties of real numbers and combining like terms, resulting in a simpler epression. Evaluating an epression is substituting values for the variables, resulting in a numerical value. 68

3 Chapter Test Do ou know HOW? Determine whether each relation is a function. 1. 5(0, ), (, 3), (5, 5), (, 7)6. 5(1, 0), (5, ), (0, ), (, 8)6 no es Evaluate each function for the given value of, and write the input and output f() as an ordered pair. 3. f () for 5 (, 9). f () for 5 8 (8, ) For each function, determine whether varies directl with. If so, find the constant of variation, and write the function rule. 5. es; k 5 ; no Graph each equation O Write in point-slope form an equation of the line through each pair of points. 9. (5, 8) and (0, ) 10. (1, 3) and (6, ) 8 5 ( 5) or 3 5( 1) or 1 5 ( 0) 1 5( 6) 87

4 Chapter Test (continued) Write the function rule g() for the given transformations applied to the graph of f () units down, 1. 7 units up, 1 unit left 3 units right g( ) 5 ( 1 1) g( ) 5 ( 3) 1 7 Graph each equation. Then describe the transformation from the parent function f () translation units right O reflection in the -ais O Graph each absolute-value inequalit. 15., u 3 u \$ u 1 5 u O Do ou UNDERSTAND? 6 6 O 17. If varies directl with and 5 18 when 5 6, what is the constant of variation? Find the value of when k 5 3; Open-Ended Graph a line that has a slope that is undefined. Answers ma var. Sample: a graph of an vertical line 19. Suppose ou manufacture and sell tarps. The table at the right displas our current sizes and prices. a. Draw a scatter plot showing the relationship between the area of a tarp and its price. Use area as the independent variable. b. Draw a trend line and write the equation. c. Reasoning Is this an accurate model? Eplain. d. Using our model, predict the price of a 50 ft tarp. b. Equations should be close to c. Yes; all the points are ver close to the line, so the linear model is accurate. d. about \$10.0 Size (ft ) Price \$1.39 \$1.99 \$3.19 \$.79 \$7.69 \$7.99 \$

5 Chapter 3 Test Do ou know HOW? Solve each sstem b substitution or elimination. 1. e e 6 51 no solution (, 1) (, 6) e Graph the solution of each sstem.. e \$ 1 3, 5. e 1 # # 6. e. 1 # You have 13 bills in our wallet in \$1, \$5, and \$10 bills. There are twice as man \$1 bills as \$5 bills. The number of \$10 bills is one more than the number of \$5 bills. How man of each bill do ou have? How much mone do ou have? si \$1 bills, three \$5 bills, four \$10 bills; \$61 Graph the sstem of constraints. Identif all vertices. Find the values of and that maimize or minimize the objective function. Then find the maimum or minimum value. # # 1 8 C(, 3) B(0, ) \$ 0, \$ 0 Maimize for P A(0, 0) 6 D(7, 0) ma P at (7, 0)

6 Chapter 3 Test (continued) What is the solution of the sstem represented b the matri? C 3 1 0S (, 1, 3) (1,, 3) (3,, 1) (1, 3, ) C Do ou UNDERSTAND? 10. Writing Eplain how ou determine whether a sstem of linear equations is independent, dependent, or inconsistent without graphing the lines. Rewrite both equations in slope-intercept form. If the lines have the same slope and same -intercept, then the are equations of the same line, and the sstem is dependent. If the lines have the same slope but different -intercepts, the are parallel lines, and the sstem is inconsistent. If the lines have different slopes, then the sstem is independent. 11. Mechanic A charges \$5 for car repairs and \$80 for each hour spent on our car. Mechanic B charges \$60 for repairs and \$60 for each hour spent on our car. a. If our car takes 5 hours to repair, which mechanic charges the least mone? Mechanic B b. How much will it cost ou to have the work done b the less epensive mechanic? \$ At a bookstore, ou spend \$76 on 11 books and magazines. Books cost \$8 each and magazines cost \$5 each. Write a matri that represents this sstem. How man books and how man magazines did ou bu? B ` 11 R ; 7 books, magazines Reasoning The sum of three numbers is 15. The second number is twice the third number. Do ou have enough information to determine the three numbers? If so, what are the three numbers? If not, what information do ou still need? No; ou need a third equation that defines another relationship between two or three of the numbers. 68

7 Chapter Test Do ou know HOW? Identif the verte, the ais of smmetr, the maimum or minimum value, and the domain and the range of each function ( ) 1 6 verte 5 (, 6); ais of smmetr 5 ; minimum 5 6; domain 5 all real numbers; range 5 all real numbers L 6. 5( 1 ) 3 verte 5 (, 3); ais of smmetr 5; maimum 53; domain 5 all real numbers; range = all real numbers K 3] O 10 O 8 Factor each epression. 5. c 1 c g 9 (c 1 1) (g 1 7)(g 7) Use a graphing calculator to solve each equation. Give each answer to at most two decimal places and and 51.9 Complete the square j j 9 81 Evaluate the discriminant for each equation. Determine the number of real solutions ; 0 real solutions 8; real solutions Plot each comple number and find its absolute value i! i 8 8i imaginar ais i real ais 8 O i 7 i 8i imaginar ais i real ais 8 O i 8i 97 8i

8 Chapter Test (continued) Find all solutions to each quadratic equation i, 1 3 i Solve each sstem b graphing "11 3 i, 1 3 "11 3 i d d, 1. O O Do ou UNDERSTAND? 19. The parabolic path of a hit tennis ball can be modeled b the table at the right. The top of the net is at (, 10). a. Find a quadratic model for the data b. Will the ball go over the net? If not, will it hit the net on the wa up or the wa down? No; it will hit the net on the wa down Writing Eplain the relationship between the -intercepts of quadratic function and the zeros of a quadratic function. The are the same thing because the -intercepts are the -coordinates where the quadratic function equals zero. 1. The period of a pendulum is the time the pendulum takes to swing back and forth. The function l t relates the length l in feet of a pendulum to the period t. a. If a pendulum is 30 ft long, what is the period of the pendulum in seconds? b. Reasoning Wh does onl one of the solutions work for this problem? The other solution is negative and ou cannot have negative time. t s 98

9 Chapter 5 Test Do ou know HOW? Write each polnomial in standard form. Then classif it b degree and b number of terms ; quintic trinomial ; cubic, terms Determine the end behavior of the graph of each polnomial function up and up down and up Find the zeros of each function. State the multiplicit of multiple zeros ( 1 )( 3) multiplicit 1; 3 multiplicit 0 multiplicit ; multiplicit 1 Find the real solutions of each equation using a graphing calculator. Where necessar, round to the nearest hundredth , 0.86 Divide using long division. Check our answers. 9. ( ) ( 1 ) 10. ( ) ( 1 1) 1, R , R 7 Write a polnomial function with rational coefficients so that P() = 0 has the given roots ,, 6 1. i,! P() P() 5 Find all the zeros of each function , i, i 3, 3, "5, "5 97

10 Chapter 5 Test (continued) Epand each binomial. 15. ( 1 ) ( 1 3) Find a cubic function to model the data in the table. Let represent ears after N Births in the United States Determine the cubic function that is obtained from the parent function = 3 after each sequence of transformations. 18. a vertical stretch b a factor of 3; a reflection across the -ais; and a horizontal translation units right 53( ) 3 Year SOURCE: Births (millions) a reflection across the -ais; a horizontal translation units left; and a vertical translation 6 units down 5( 1 ) 3 6 Do ou UNDERSTAND? 0. The product of three integers is 56. The second number is twice the first number. The third number is five more than the first number. What are the three numbers?,, 7 1. What is P() given that P() ? Use snthetic division and the Remainder Theorem. P() Open-Ended Write a polnomial function of degree 3 with rational coefficients and eactl one real zero. List all of the zeros of the function. Answers will var. Sample: ; zeros: 3, i "5, i"5 1. A cubic bo is in. on each side. If each dimension is increased b in., what is the polnomial function modeling the new volume V? V in. 3 98

11 Chapter 11 Test Do ou know HOW? 1. Your brother is ordering 5 pizzas for the famil. There are 18 different kinds of pizza. How man different was could he order 5 different kinds of pizzas? 8568 was A bo contains 8 blueberr muffins, 6 banana muffins, and pumpkin muffins. You pick one muffin from the bo at random. Find each theoretical probabilit.. P(banana) 1 3. P(not pumpkin) 7. P(banana or pumpkin) J and K are independent events. P(J) = 1 and P(K) = 3. Find P(J and K) A compan is testing a new sunscreen to see if it is more likel to cause skin irritation that the sunscreen it currentl sells. The results of the test are shown in the contingenc table. Used new sunscreen Used current sunscreen Totals Skin irritation No skin irritation Totals The compan decides to make and sell the new sunscreen. Based on the results of the test, did the compan make a good decision? Eplain. Answers ma var. Sample: Yes; about out of 0 people who use the new sunscreen have skin irritation, compared to about 3 out of 0 people who use the current sunscreen. Based on this stud, the new sunscreen is no more likel to cause skin irritation than the current sunscreen, so the compan made a good decision. For Eercises 7 and 8, use the following data set: Find the mean, variance, and standard deviation for the data set. 31; 18.8; Within how man standard deviations of the mean do all of the data values fall? All of the values fall within standard deviations of the mean. 107

13 Chapter 1 Test Do ou know HOW? Find each sum or difference c d 1 c1 1 5 d. c d c 1 6 d c 7 6 d 5 3 c 1 0 d Find the value of each variable.. c d 1 c1 z d 5 c z d 5. c d 5 c d 5 1; 5 3; z 5 5 3; 5 ; z 5 5 Find each product c 1 dc5 3 d 7. c dc 5 1 d 8. f1 3g c d 1 6 c d c d f10 19g Do ou UNDERSTAND? 9. Writing Describe the matri operations that ou must use to solve the following matri equation. Then find the value of X. c 1 d 1 X 5 c 3 d First, multipl b the scalar. Then, use the Subtraction Propert of Equalit to isolate the variable matri. Subtract corresponding elements. Finall, multipl each side b 1 7 and simplif; X 5 c 3 5 d 67

14 Chapter 1 Test (continued) Do ou know HOW? Determine whether the following matrices are multiplicative inverses. 10. c d, c1 d 11. c d, c d 1. c 1 d, no es es Use inverse matrices to find the solution of each matri equation c 3 8 d X 5 c5 X 5 c 10 d d 1. c3 1 5 X 5 c 7 1 d 17 3 d X 5 c5 d 15. c d X 5 c 1 11 d X 5 c 5 d Use matrices to solve the following sstems of equations e ; e ; z z z ; 5 3; z 5 7 Do ou UNDERSTAND? 19. Roger and Clarissa each sold boes of cookies for a fundraiser. The sold large and small boes for different prices. Roger sold 1 large boes and 8 small boes for a total of \$ Clarissa sold 16 large boes and 11 small boes for a total of \$ Use a sstem of two equations and matrices to find the price of a large bo and a small bo. large: \$3.00; small: \$.50 68

### Polynomial and Rational Functions

Chapter Section.1 Quadratic Functions Polnomial and Rational Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Course Number Instructor Date Important

### 135 Final Review. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.

13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, -6); P2 = (7, -2) 2 12 2 12 3 Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the

### Practice for Final Disclaimer: The actual exam is not a mirror of this. These questions are merely an aid to help you practice 1 2)

Practice for Final Disclaimer: The actual eam is not a mirror of this. These questions are merel an aid to help ou practice Solve the problem. 1) If m varies directl as p, and m = 7 when p = 9, find m

### FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) -

### 1. a. standard form of a parabola with. 2 b 1 2 horizontal axis of symmetry 2. x 2 y 2 r 2 o. standard form of an ellipse centered

Conic Sections. Distance Formula and Circles. More on the Parabola. The Ellipse and Hperbola. Nonlinear Sstems of Equations in Two Variables. Nonlinear Inequalities and Sstems of Inequalities In Chapter,

### Reteaching Masters. To jump to a location in this book. 1. Click a bookmark on the left. To print a part of the book. 1. Click the Print button.

Reteaching Masters To jump to a location in this book. Click a bookmark on the left. To print a part of the book. Click the Print button.. When the Print window opens, tpe in a range of pages to print.

### Unit 1 Study Guide Systems of Linear Equations and Inequalities. Part 1: Determine if an ordered pair is a solution to a system

Unit Stud Guide Sstems of Linear Equations and Inequalities 6- Solving Sstems b Graphing Part : Determine if an ordered pair is a solution to a sstem e: (, ) Eercises: substitute in for and - in for in

### Solving Systems Using Tables and Graphs

- Think About a Plan Solving Sstems Using Tables and Graphs Sports You can choose between two tennis courts at two universit campuses to learn how to pla tennis. One campus charges \$ per hour. The other

### M122 College Algebra Review for Final Exam

M1 College Algebra Review for Final Eam Revised Fall 015 for College Algebra Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature

Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In

### 2.3 Writing Equations of Lines

. Writing Equations of Lines In this section ou will learn to use point-slope form to write an equation of a line use slope-intercept form to write an equation of a line graph linear equations using the

### 1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model

. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses

### Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form

SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving

### Zeros of Polynomial Functions. The Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra. zero in the complex number system.

_.qd /7/ 9:6 AM Page 69 Section. Zeros of Polnomial Functions 69. Zeros of Polnomial Functions What ou should learn Use the Fundamental Theorem of Algebra to determine the number of zeros of polnomial

### Higher. Polynomials and Quadratics 64

hsn.uk.net Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 64 1 Quadratics 64 The Discriminant 66 3 Completing the Square 67 4 Sketching Parabolas 70 5 Determining

. Quadratic Functions 9. Quadratic Functions You ma recall studing quadratic equations in Intermediate Algebra. In this section, we review those equations in the contet of our net famil of functions: the

### The Slope-Intercept Form

7.1 The Slope-Intercept Form 7.1 OBJECTIVES 1. Find the slope and intercept from the equation of a line. Given the slope and intercept, write the equation of a line. Use the slope and intercept to graph

### M122 College Algebra Review for Final Exam

M122 College Algebra Review for Final Eam Revised Fall 2007 for College Algebra in Contet All answers should include our work (this could be a written eplanation of the result, a graph with the relevant

### Graphing Linear Equations

6.3 Graphing Linear Equations 6.3 OBJECTIVES 1. Graph a linear equation b plotting points 2. Graph a linear equation b the intercept method 3. Graph a linear equation b solving the equation for We are

### Filling in Coordinate Grid Planes

Filling in Coordinate Grid Planes A coordinate grid is a sstem that can be used to write an address for an point within the grid. The grid is formed b two number lines called and that intersect at the

### Exponential and Logarithmic Functions

Chapter 3 Eponential and Logarithmic Functions Section 3.1 Eponential Functions and Their Graphs Objective: In this lesson ou learned how to recognize, evaluate, and graph eponential functions. Course

### 8.7 Systems of Non-Linear Equations and Inequalities

8.7 Sstems of Non-Linear Equations and Inequalities 67 8.7 Sstems of Non-Linear Equations and Inequalities In this section, we stud sstems of non-linear equations and inequalities. Unlike the sstems of

### Study Guide and Intervention Workbook

Stud Guide and Intervention Workbook To the Student This Stud Guide and Intervention Workbook gives ou additional eamples and problems for the concept eercises in each lesson. The eercises are designed

### MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets

### Lesson 9.1 Solving Quadratic Equations

Lesson 9.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with a. One -intercept and all nonnegative y-values. b. The verte in the third quadrant and no -intercepts. c. The verte

### Florida Algebra I EOC Online Practice Test

Florida Algebra I EOC Online Practice Test 1 Directions: This practice test contains 65 multiple-choice questions. Choose the best answer for each question. Detailed answer eplanations appear at the end

### Translating Points. Subtract 2 from the y-coordinates

CONDENSED L E S S O N 9. Translating Points In this lesson ou will translate figures on the coordinate plane define a translation b describing how it affects a general point (, ) A mathematical rule that

### Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

### 4 Non-Linear relationships

NUMBER AND ALGEBRA Non-Linear relationships A Solving quadratic equations B Plotting quadratic relationships C Parabolas and transformations D Sketching parabolas using transformations E Sketching parabolas

### LESSON EIII.E EXPONENTS AND LOGARITHMS

LESSON EIII.E EXPONENTS AND LOGARITHMS LESSON EIII.E EXPONENTS AND LOGARITHMS OVERVIEW Here s what ou ll learn in this lesson: Eponential Functions a. Graphing eponential functions b. Applications of eponential

### More Equations and Inequalities

Section. Sets of Numbers and Interval Notation 9 More Equations and Inequalities 9 9. Compound Inequalities 9. Polnomial and Rational Inequalities 9. Absolute Value Equations 9. Absolute Value Inequalities

### North Carolina Community College System Diagnostic and Placement Test Sample Questions

North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

### Quadratic Functions. MathsStart. Topic 3

MathsStart (NOTE Feb 2013: This is the old version of MathsStart. New books will be created during 2013 and 2014) Topic 3 Quadratic Functions 8 = 3 2 6 8 ( 2)( 4) ( 3) 2 1 2 4 0 (3, 1) MATHS LEARNING CENTRE

A. THE STANDARD PARABOLA Graphing Quadratic Functions The graph of a quadratic function is called a parabola. The most basic graph is of the function =, as shown in Figure, and it is to this graph which

### Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

### Objectives. By the time the student is finished with this section of the workbook, he/she should be able

QUADRATIC FUNCTIONS Completing the Square..95 The Quadratic Formula....99 The Discriminant... 0 Equations in Quadratic Form.. 04 The Standard Form of a Parabola...06 Working with the Standard Form of a

### Summer Review For Students Entering Algebra 2

Summer Review For Students Entering Algebra Board of Education of Howard Count Frank Aquino Chairman Ellen Flnn Giles Vice Chairman Larr Cohen Allen Der Sandra H. French Patricia S. Gordon Janet Siddiqui

### INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1

Chapter 1 INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4 This opening section introduces the students to man of the big ideas of Algebra 2, as well as different was of thinking and various problem solving strategies.

### Alex and Morgan were asked to graph the equation y = 2x + 1

Which is better? Ale and Morgan were asked to graph the equation = 2 + 1 Ale s make a table of values wa Morgan s use the slope and -intercept wa First, I made a table. I chose some -values, then plugged

### Polynomial and Rational Functions

Chapter 5 Polnomial and Rational Functions Section 5.1 Polnomial Functions Section summaries The general form of a polnomial function is f() = a n n + a n 1 n 1 + +a 1 + a 0. The degree of f() is the largest

### LINEAR FUNCTIONS. Form Equation Note Standard Ax + By = C A and B are not 0. A > 0

LINEAR FUNCTIONS As previousl described, a linear equation can be defined as an equation in which the highest eponent of the equation variable is one. A linear function is a function of the form f ( )

### SOLVING SYSTEMS OF EQUATIONS

SOLVING SYSTEMS OF EQUATIONS 4.. 4..4 Students have been solving equations even before Algebra. Now the focus on what a solution means, both algebraicall and graphicall. B understanding the nature of solutions,

### Lesson 6: Linear Functions and their Slope

Lesson 6: Linear Functions and their Slope A linear function is represented b a line when graph, and represented in an where the variables have no whole number eponent higher than. Forms of a Linear Equation

### SECTION 5-1 Exponential Functions

354 5 Eponential and Logarithmic Functions Most of the functions we have considered so far have been polnomial and rational functions, with a few others involving roots or powers of polnomial or rational

### Rational Functions. 7.1 A Rational Existence. 7.2 A Rational Shift in Behavior. 7.3 A Rational Approach. 7.4 There s a Hole In My Function, Dear Liza

Rational Functions 7 The ozone laer protects Earth from harmful ultraviolet radiation. Each ear, this laer thins dramaticall over the poles, creating ozone holes which have stretched as far as Australia

### Let (x 1, y 1 ) (0, 1) and (x 2, y 2 ) (x, y). x 0. y 1. y 1 2. x x Multiply each side by x. y 1 x. y x 1 Add 1 to each side. Slope-Intercept Form

8 (-) Chapter Linear Equations in Two Variables and Their Graphs In this section Slope-Intercept Form Standard Form Using Slope-Intercept Form for Graphing Writing the Equation for a Line Applications

### GRAPHS OF RATIONAL FUNCTIONS

0 (0-) Chapter 0 Polnomial and Rational Functions. f() ( 0) ( 0). f() ( 0) ( 0). f() ( 0) ( 0). f() ( 0) ( 0) 0. GRAPHS OF RATIONAL FUNCTIONS In this section Domain Horizontal and Vertical Asmptotes Oblique

### 11.7 MATHEMATICAL MODELING WITH QUADRATIC FUNCTIONS. Objectives. Maximum Minimum Problems

a b Objectives Solve maimum minimum problems involving quadratic functions. Fit a quadratic function to a set of data to form a mathematical model, and solve related applied problems. 11.7 MATHEMATICAL

### 5.1. A Formula for Slope. Investigation: Points and Slope CONDENSED

CONDENSED L E S S O N 5.1 A Formula for Slope In this lesson ou will learn how to calculate the slope of a line given two points on the line determine whether a point lies on the same line as two given

### SAMPLE. Polynomial functions

Objectives C H A P T E R 4 Polnomial functions To be able to use the technique of equating coefficients. To introduce the functions of the form f () = a( + h) n + k and to sketch graphs of this form through

### Systems of Equations. from Campus to Careers Fashion Designer

Sstems of Equations from Campus to Careers Fashion Designer Radius Images/Alam. Solving Sstems of Equations b Graphing. Solving Sstems of Equations Algebraicall. Problem Solving Using Sstems of Two Equations.

### MATH 185 CHAPTER 2 REVIEW

NAME MATH 18 CHAPTER REVIEW Use the slope and -intercept to graph the linear function. 1. F() = 4 - - Objective: (.1) Graph a Linear Function Determine whether the given function is linear or nonlinear..

### Florida Algebra I EOC Online Practice Test

Florida Algebra I EOC Online Practice Test Directions: This practice test contains 65 multiple-choice questions. Choose the best answer for each question. Detailed answer eplanations appear at the end

### 5.3 Graphing Cubic Functions

Name Class Date 5.3 Graphing Cubic Functions Essential Question: How are the graphs of f () = a ( - h) 3 + k and f () = ( 1_ related to the graph of f () = 3? b ( - h) 3 ) + k Resource Locker Eplore 1

### Answers (Lesson 3-1) Study Guide and Intervention. Study Guide and Intervention (continued) Solving Systems of Equations by Graphing

Glencoe/McGraw-Hill A Glencoe Algebra - NAME DATE PERID Stud Guide and Intervention Solving Sstems of Equations b Graphing Graph Sstems of Equations A sstem of equations is a set of two or more equations

### Q (x 1, y 1 ) m = y 1 y 0

. Linear Functions We now begin the stud of families of functions. Our first famil, linear functions, are old friends as we shall soon see. Recall from Geometr that two distinct points in the plane determine

### Students Currently in Algebra 2 Maine East Math Placement Exam Review Problems

Students Currently in Algebra Maine East Math Placement Eam Review Problems The actual placement eam has 100 questions 3 hours. The placement eam is free response students must solve questions and write

### EQUATIONS OF LINES IN SLOPE- INTERCEPT AND STANDARD FORM

. Equations of Lines in Slope-Intercept and Standard Form ( ) 8 In this Slope-Intercept Form Standard Form section Using Slope-Intercept Form for Graphing Writing the Equation for a Line Applications (0,

### Linear Equations in Two Variables

Section. Sets of Numbers and Interval Notation 0 Linear Equations in Two Variables. The Rectangular Coordinate Sstem and Midpoint Formula. Linear Equations in Two Variables. Slope of a Line. Equations

Quadratic Functions Unit 5 Unit Overview In this unit ou will stud a variet of was to solve quadratic functions and appl our learning to analzing real world problems. Academic Vocabular Add these words

### COGNITIVE TUTOR ALGEBRA

COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,

### POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

### 6. The given function is only drawn for x > 0. Complete the function for x < 0 with the following conditions:

Precalculus Worksheet 1. Da 1 1. The relation described b the set of points {(-, 5 ),( 0, 5 ),(,8 ),(, 9) } is NOT a function. Eplain wh. For questions - 4, use the graph at the right.. Eplain wh the graph

### Simplification of Rational Expressions and Functions

7.1 Simplification of Rational Epressions and Functions 7.1 OBJECTIVES 1. Simplif a rational epression 2. Identif a rational function 3. Simplif a rational function 4. Graph a rational function Our work

### Transformations of Function Graphs

- - - 0 - - - - - - - Locker LESSON.3 Transformations of Function Graphs Teas Math Standards The student is epected to: A..C Analze the effect on the graphs of f () = when f () is replaced b af (), f (b),

0 The Quadratic Function TERMINOLOGY Ais of smmetr: A line about which two parts of a graph are smmetrical. One half of the graph is a reflection of the other Coefficient: A constant multiplied b a pronumeral

### Graphing Linear Equations in Slope-Intercept Form

4.4. Graphing Linear Equations in Slope-Intercept Form equation = m + b? How can ou describe the graph of the ACTIVITY: Analzing Graphs of Lines Work with a partner. Graph each equation. Find the slope

### 1.2 GRAPHS OF EQUATIONS

000_00.qd /5/05 : AM Page SECTION. Graphs of Equations. GRAPHS OF EQUATIONS Sketch graphs of equations b hand. Find the - and -intercepts of graphs of equations. Write the standard forms of equations of

### If (a)(b) 5 0, then a 5 0 or b 5 0.

chapter Algebra Ke words substitution discriminant completing the square real and distinct imaginar rational verte parabola maimum minimum surd irrational rationalising the denominator Section. Quadratic

### Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities

Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.

### SECTION 2-5 Combining Functions

2- Combining Functions 16 91. Phsics. A stunt driver is planning to jump a motorccle from one ramp to another as illustrated in the figure. The ramps are 10 feet high, and the distance between the ramps

SKILL Are You Read? Simplif Radical Epressions Teaching Skill Objective Simplif radical epressions. Review with students the definition of simplest form. Ask: Is written in simplest form? (No) Wh or wh

### 2-5. The Graph of y = kx 2. Vocabulary. Rates of Change. Lesson. Mental Math

Chapter 2 Lesson 2-5 The Graph of = k 2 BIG IDEA The graph of the set of points (, ) satisfing = k 2, with k constant, is a parabola with verte at the origin and containing the point (1, k). Vocabular

### Contents. How You May Use This Resource Guide

Contents How You Ma Use This Resource Guide ii 9 Fractional and Quadratic Equations 1 Worksheet 9.1: Similar Figures.......................... 5 Worksheet 9.: Stretch of a Spring........................

### C3: Functions. Learning objectives

CHAPTER C3: Functions Learning objectives After studing this chapter ou should: be familiar with the terms one-one and man-one mappings understand the terms domain and range for a mapping understand the

88 Linear and Quadratic Functions. Quadratic Functions You ma recall studing quadratic equations in Intermediate Algebra. In this section, we review those equations in the contet of our net famil of functions:

### CHAPTER 9. Polynomials

CHAPTER 9 In this chapter ou epand our knowledge of families of functions to include polnomial functions. As ou investigate the equation! graph connection for polnomials, ou will learn how to search for

### Use order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS

ORDER OF OPERATIONS In the following order: 1) Work inside the grouping smbols such as parenthesis and brackets. ) Evaluate the powers. 3) Do the multiplication and/or division in order from left to right.

### Introduction - Algebra I

LIFORNI STNRS TEST lgebra I Introduction - lgebra I The following released test questions are taken from the lgebra I Standards Test. This test is one of the alifornia Standards Tests administered as part

### 10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED

CONDENSED L E S S O N 10.1 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

### REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95

REVIEW SHEETS INTERMEDIATE ALGEBRA MATH 95 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course. The sheets

### 2.4 Inequalities with Absolute Value and Quadratic Functions

08 Linear and Quadratic Functions. Inequalities with Absolute Value and Quadratic Functions In this section, not onl do we develop techniques for solving various classes of inequalities analticall, we

### Essential Question How can you use completing the square to solve a quadratic equation?

9.4 Solving Quadratic Equations Completing the Square Essential Question How can ou use completing the square to solve a quadratic equation? Work with a partner. a. Write the equation modeled the algera

### Graphing Nonlinear Systems

10.4 Graphing Nonlinear Sstems 10.4 OBJECTIVES 1. Graph a sstem of nonlinear equations 2. Find ordered pairs associated with the solution set of a nonlinear sstem 3. Graph a sstem of nonlinear inequalities

### QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

CHAPTER 86 5 CHAPTER TABLE F CNTENTS 5- Real Roots of a Quadratic Equation 5-2 The Quadratic Formula 5-3 The Discriminant 5-4 The Comple Numbers 5-5 perations with Comple Numbers 5-6 Comple Roots of a

### THE PARABOLA section. Developing the Equation

80 (-0) Chapter Nonlinear Sstems and the Conic Sections. THE PARABOLA In this section Developing the Equation Identifing the Verte from Standard Form Smmetr and Intercepts Graphing a Parabola Maimum or

### 1.6. Determine a Quadratic Equation Given Its Roots. Investigate

1.6 Determine a Quadratic Equation Given Its Roots Bridges like the one shown often have supports in the shape of parabolas. If the anchors at either side of the bridge are 4 m apart and the maximum height

### 2 Analysis of Graphs of

ch.pgs1-16 1/3/1 1:4 AM Page 1 Analsis of Graphs of Functions A FIGURE HAS rotational smmetr around an ais I if it coincides with itself b all rotations about I. Because of their complete rotational smmetr,

### a > 0 parabola opens a < 0 parabola opens

Objective 8 Quadratic Functions The simplest quadratic function is f() = 2. Objective 8b Quadratic Functions in (h, k) form Appling all of Obj 4 (reflections and translations) to the function. f() = a(

8 Coordinate Geometr Negative gradients: m < 0 Positive gradients: m > 0 Chapter Contents 8:0 The distance between two points 8:0 The midpoint of an interval 8:0 The gradient of a line 8:0 Graphing straight

### Advanced Algebra 2. I. Equations and Inequalities

Advanced Algebra 2 I. Equations and Inequalities A. Real Numbers and Number Operations 6.A.5, 6.B.5, 7.C.5 1) Graph numbers on a number line 2) Order real numbers 3) Identify properties of real numbers

### ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section

ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 5-3.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 6-4.2 Solving Equations by

### HIBBING COMMUNITY COLLEGE COURSE OUTLINE

HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,

### NAME DATE PERIOD. 11. Is the relation (year, percent of women) a function? Explain. Yes; each year is

- NAME DATE PERID Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. No; in the

### Essential Question How can you describe the graph of the equation Ax + By = C? Number of adult tickets. adult

3. Graphing Linear Equations in Standard Form Essential Question How can ou describe the graph of the equation A + B = C? Using a Table to Plot Points Work with a partner. You sold a total of \$16 worth

### Solving Systems of Linear Equations

5 Solving Sstems of Linear Equations 5. Solving Sstems of Linear Equations b Graphing 5. Solving Sstems of Linear Equations b Substitution 5.3 Solving Sstems of Linear Equations b Elimination 5. Solving