17
Erie, Pennsylvania BigIdeasLearning.com BIG IDEAS MATH ® Ron Larson and Laurie Boswell TEXAS EDITION
Erie, PennsylvaniaBigIdeasLearning.com
B I G I D E A S
MATH®
Ron Larson and Laurie Boswell
TEXAS EDITION
Big Ideas Learning, LLC
1762 Norcross Road
Erie, PA 16510-3838
USA
For product information and customer support, contact Big Ideas Learning
at 1-877-552-7766 or visit us at BigIdeasLearning.com.
Copyright © 2015 by Big Ideas Learning, LLC. All rights reserved.
No part of this work may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including, but not limited to, photocopying and recording, or
by any information storage or retrieval system, without prior written permission of
Big Ideas Learning, LLC unless such copying is expressly permitted by copyright law.
Address inquiries to Permissions, Big Ideas Learning, LLC, 1762 Norcross Road,
Erie, PA 16510.
Big Ideas Learning and Big Ideas Math are registered trademarks of Larson Texts, Inc.
Printed in the U.S.A.
ISBN 13: 978-1-60840-814-6
ISBN 10: 1-60840-814-0
2 3 4 5 6 7 8 9 10 WEB 18 17 16 15 14
iii
Dr. Ron Larson and Dr. Laurie Boswell began writing together in 1992. Since that time, they have authored over two dozen textbooks. In their collaboration, Ron is primarily responsible for the student edition while Laurie is primarily responsible for the teaching edition.
Ron Larson, Ph.D., is well known as the lead author of a comprehensive program for mathematics that spans middle school, high school, and college courses. He holds the distinction of Professor Emeritus from Penn State Erie, The Behrend College, where he taught for nearly 40 years. He received his Ph.D. in mathematics from the University of Colorado. Dr. Larson’s numerous professional activities keep him actively involved in the mathematics education community and allow him to fully understand the needs of students, teachers, supervisors, and administrators.
Laurie Boswell, Ed.D., is the Head of School and a mathematics teacher at the Riverside School in Lyndonville, Vermont. Dr. Boswell is a recipient of the Presidential Award for Excellence in Mathematics Teaching and has taught mathematics to students at all levels, from elementary through college. Dr. Boswell was a Tandy Technology Scholar and served on the NCTM Board of Directors from 2002 to 2005. She currently serves on the board of NCSM and is a popular national speaker.
Authors
iv
Welcome to Big Ideas Math Algebra 1. From start to fi nish, this program was designed with you, the learner, in mind.
As you work through the chapters in your Algebra 1 course, you will be encouraged to think and to make conjectures while you persevere through challenging problems and exercises. You will make errors—and that is ok! Learning and understanding occur when you make errors and push through mental roadblocks to comprehend and solve new and challenging problems.
In this program, you will also be required to explain your thinking and your analysis of diverse problems and exercises. Being actively involved in learning will help you develop mathematical reasoning and use it to solve math problems and work through other everyday challenges.
We wish you the best of luck as you explore Algebra 1. We are excited to be a part of your preparation for the challenges you will face in the remainder of your high school career and beyond.
For the Student
40
Maintaining Mathematical ProficiencyMaintaining Mathematical ProficiencyGraphing Linear Equations (A.3.C)
Example 1 Graph y = −x − 1.
Step 1 Make a table of values.
x y = −x − 1 y (x, y)
−1 y = −(−1) − 1 0 (−1, 0)
0 y = −(0) − 1 −1 (0, −1)
1 y = −(1) − 1 −2 (1, −2)
2 y = −(2) − 1 −3 (2, −3)
Step 2 Plot the ordered pairs.
Step 3 Draw a line through the points.
Graph the linear equation.
1. y = 2x − 3 2. y = −3x + 4
3. y = − 1 — 2 x − 2 4. y = x + 5
Evaluating Expressions (A.11.B)
Example 2 Evaluate 2x2 + 3x − 5 when x = −1.
2x2 + 3x − 5 = 2(−1)2 + 3(−1) − 5 Substitute −1 for x.
= 2(1) + 3(−1) − 5 Evaluate the power.
= 2 − 3 − 5 Multiply.
= −6 Subtract.
Evaluate the expression when x = −2.
5. 5x2 − 9 6. 3x2 + x − 2
7. −x2 + 4x + 1 8. x2 + 8x + 5
9. −2x2 − 4x + 3 10. −4x2 + 2x − 6
11. ABSTRACT REASONING Complete the table. Find a pattern in the differences of
consecutive y-values. Use the pattern to write an expression for y when x = 6.
x 1 2 3 4 5
y = ax2
Mathematical Thinking: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
8.1 Graphing f (x) = ax2
8.2 Graphing f (x) = ax2 + c8.3 Graphing f (x) = ax2 + bx + c8.4 Graphing f (x) = a(x − h)2 + k8.5 Using Intercept Form
8.6 Comparing Linear, Exponential, and Quadratic Functions
8 Graphing Quadratic Functions
Roller Coaster (p. 434)
Satellite Dish (p. 443)
Firework Explosion (p. 423)
Garden Waterfalls (p. 416)
Town Population (p. 450)
Satellite Dish (p 443)
Roller Coaster (p. 434)
Firework Explosion (p 423)
GGaGa ddrdenen WWWatatererfffallllllss (((p. 4141416)6)6)
x
y
2
−4
2
(−1, 0)(0, −1) (1, −2)
(2, −3)
x22
2
y = −x − 1
Town Pop lulatiion ((p 45 )0)
SEE the Big Idea
404 Chapter 8 Graphing Quadratic Functions
Mathematical Mathematical ThinkingThinkingProblem-Solving Strategies
Mathematically profi cient students use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. (A.1.B)
1. y = −x2 2. y = 2x2 3. f (x) = 2x2 + 1 4. f (x) = 2x2 − 1
5. f (x) = 1 —
2 x2 + 4x + 3 6. f (x) =
1 —
2 x2 − 4x + 3 7. y = −2(x + 1)2 + 1 8. y = −2(x − 1)2 + 1
9. How are the graphs in Monitoring Progress Questions 1−8 similar? How are they different?
Graphing the Parent Quadratic Function
Graph the parent quadratic function y = x2. Then describe its graph.
SOLUTIONThe function is of the form y = ax2, where a = 1. By plotting several points, you can see
that the graph is U-shaped, as shown.
4
6
8
10
y
2
Trying Special Cases When solving a problem in mathematics, it can be helpful to try special cases of the
original problem. For instance, in this chapter, you will learn to graph a quadratic
function of the form f (x) = ax2 + bx + c. The problem-solving strategy used is to
fi rst graph quadratic functions of the form f (x) = ax2. From there, you progress to
other forms of quadratic functions.
f (x) = ax2 Section 8.1
f (x) = ax2 + c Section 8.2
f (x) = ax2 + bx + c Section 8.3
f (x) = a(x − h)2 + k Section 8.4
Core Core ConceptConcept
HS
TX
_AL
G1_
PE
_08.
OP
•
Mar
ch 19
, 201
4 1:4
4 PM
FIN
AL
page
s
404 Chapter 8 Graphing Quadratic Functions
1. y = −x2 2. y = 2x22 2 3. f(ff x) = 2x22 2 + 1 4. f(ff x) = 2x22 2 − 1
5. f(ff x) = 1—2
x2 + 4x + 3 6. f(ff x) = 1—2
x2 − 4x + 3 7. y = −2(x + 1)2 + 1 8. y = −2(x − 1)2 + 1
9. How are the graphs in Monitoring Progress Questions 1−8 similar? How are they different?
44
66
88
10
y
2
408 Chapter 8 Graphing Quadratic Functions Section 8.1 Graphing f(x) = ax2 409
Tutorial Help in English and Spanish at BigIdeasMath.comExercises8.1
In Exercises 3 and 4, identify characteristics of the quadratic function and its graph. (See Example 1.)
3.
−2
−6
1
x42−2
y
4.
4
8
12
x84−4−8
y
In Exercises 5–16, graph the function. Compare the graph to the graph of f (x) = x2. (See Examples 2, 3, and 4.)
5. g(x) = 6x2 6. b(x) = 2.5x2
7. h(x) = 1 — 4 x2 8. j(x) = 0.75x2
9. m(x) = −2x2 10. q(x) = − 9 — 2 x2
11. k(x) = −0.2x2 12. p(x) = − 2 — 3 x2
13. n(x) = (2x)2 14. d(x) = (−4x)2
15. c(x) = ( − 1 — 3 x ) 2 16. r(x) = (0.1x)2
17. ERROR ANALYSIS Describe and correct the error in
graphing and comparing y = x2 and y = 0.5x2.
x
y = x2
y = 0.5x2
y
The graphs have the same vertex and the same
axis of symmetry. The graph of y = 0.5x2 is
narrower than the graph of y = x2.
✗
18. MODELING WITH MATHEMATICS The arch support of
a bridge can be modeled by y = −0.0012x2, where x
and y are measured in feet. Find the height and width
of the arch. (See Example 5.)
50
x350 45025050−50−250−350−450
y
−150
−250
−350
19. PROBLEM SOLVING The breaking strength z
(in pounds) of a manila rope can be modeled by
z = 8900d2, where d is the diameter (in inches)
of the rope.
a. Describe the domain and
range of the function.
b. Graph the function using
the domain in part (a).
c. A manila rope has four times the breaking strength
of another manila rope. Does the stronger rope
have four times the diameter? Explain.
Monitoring Progress and Modeling with MathematicsMonitoring Progress and Modeling with Mathematics
1. VOCABULARY What is the U-shaped graph of a quadratic function called?
2. WRITING When does the graph of a quadratic function open up? open down?
Vocabulary and Core Concept CheckVocabulary and Core Concept Check
Graphing y = (ax)2
Graph n(x) = ( − 1 — 4 x ) 2. Compare the graph to the graph of f (x) = x2.
SOLUTION
Rewrite n. n(x) = ( − 1 — 4 x ) 2 = 1 —
16 x2
Step 1 Make a table of values.
Step 2 Plot the ordered pairs.
Step 3 Draw a smooth curve through the points.
Both graphs open up and have the same vertex, (0, 0), and the same axis of
symmetry, x = 0. The graph of n is wider than the graph of f because the graph
of n is a horizontal stretch by a factor of 4 of the graph of f.
Solving a Real-Life Problem
The diagram at the left shows the cross section of a satellite dish, where x and y are
measured in meters. Find the width and depth of the dish.
SOLUTION
Use the domain of the function to fi nd the width
of the dish. Use the range to fi nd the depth.
The leftmost point on the graph is (−2, 1), and
the rightmost point is (2, 1). So, the domain
is −2 ≤ x ≤ 2, which represents 4 meters.
The lowest point on the graph is (0, 0), and the highest points on the graph
are (−2, 1) and (2, 1). So, the range is 0 ≤ y ≤ 1, which represents 1 meter.
So, the satellite dish is 4 meters wide and 1 meter deep.
Monitoring ProgressMonitoring Progress Help in English and Spanish at BigIdeasMath.com
Graph the function. Compare the graph to the graph of f (x) = x2.
3. g(x) = 5x2 4. h(x) = 1 —
3 x2 5. p(x) = −3x2
6. q(x) = −0.1x2 7. n(x) = (3x)2 8. g(x) = ( − 1 — 2 x ) 2 9. The cross section of a spotlight can be modeled by the graph of y = 0.5x2,
where x and y are measured in inches and −2 ≤ x ≤ 2. Find the width and
depth of the spotlight.
1
2
x2−1−2
y
y = x214(−2, 1)
(0, 0)
(2, 1)
width
depth
d
x
y
−8−16 8 16
8
16
24
32
f(x) = x2 n(x) = − x 21
4 )(x −16 −8 0 8 16
n(x) 16 4 0 4 16
Core Core ConceptConceptGraphing f (x) = (ax)2
• When 0 < ∣ a ∣ < 1, the graph of f (x) = (ax)2
is a horizontal stretch of the graph of
f (x) = x2.
• When ∣ a ∣ > 1, the graph of f (x) = (ax)2 is a
horizontal shrink of the graph of f (x) = x2.x
�a � = 1 �a � > 1
0 < �a � < 1
y
Section 8.1 Graphing f(x) = ax2 405
Graphing f (x) = ax28.1
Essential QuestionEssential Question What are some of the characteristics of the
graph of a quadratic function of the form f (x) = ax2?
Graphing Quadratic Functions
Work with a partner. Graph each quadratic function. Compare each graph to the
graph of f (x) = x2.
a. g(x) = 3x2 b. g(x) = −5x2
2
4
6
8
10
x2 4 6−6 −4 −2
y
f(x) = x2
4
x2 4 6−6 −4 −2
−4
−8
−12
−16
y
f(x) = x2
c. g(x) = −0.2x2 d. g(x) = 1 —
10 x2
2
4
6
x2 4 6−6 −4 −2
−2
−4
−6
y
f(x) = x2
2
4
6
8
10
x2 4 6−6 −4 −2
y
f(x) = x2
Communicate Your AnswerCommunicate Your Answer 2. What are some of the characteristics of the graph of a quadratic function of
the form f (x) = ax2?
3. How does the value of a affect the graph of f (x) = ax2? Consider 0 < a < 1,
a > 1, −1 < a < 0, and a < −1. Use a graphing calculator to verify
your answers.
4. The fi gure shows the graph of a quadratic function
of the form y = ax2. Which of the intervals
in Question 3 describes the value of a? Explain
your reasoning.
REASONINGTo be profi cient in math, you need to make sense of quantities and their relationships in problem situations.
6
−1
−6
7
A.6.AA.7.AA.7.C
TEXAS ESSENTIAL KNOWLEDGE AND SKILLS
v
Big Ideas Math Algebra 1, Geometry, and Algebra 2 is a research-based program providing a rigorous, focused, and coherent curriculum for high school students. Ron Larson and Laurie Boswell utilized their expertise as well as the body of knowledge collected by additional expert mathematicians and researchers to develop each course. The pedagogical approach to this program follows the best practices outlined in the most prominent and widely-accepted educational research and standards, including:
Achieve, ACT, and The College Board
Adding It Up: Helping Children Learn MathematicsNational Research Council ©2001
Curriculum Focal Points and the Principles and Standards for School Mathematics ©2000National Council of Teachers of Mathematics (NCTM)
Project Based LearningThe Buck Institute
Rigor/Relevance FrameworkTM
International Center for Leadership in Education
Universal Design for Learning GuidelinesCAST ©2011
We would also like to express our gratitude to the experts who served as consultants for Big Ideas Math Algebra 1, Geometry, and Algebra 2. Their input was an invaluable asset to the development of this program.
Big Ideas Math High School Research
Carolyn BrilesMathematics TeacherLeesburg, Virginia
Jean CarwinMath Specialist/TOSASnohomish, Washington
Alice Fisher Instructional Support Specialist, RUSMPHouston, Texas
Kristen KarbonCurriculum and Assessment CoordinatorTroy, Michigan
Anne Papakonstantinou, Ed.D.Project Director, RUSMPHouston, Texas
Richard Parr Executive Director, RUSMPHouston, Texas
Melissa Ruffi nMaster of EducationAustin, Texas
Connie Schrock, Ph.D.Mathematics ProfessorEmporia, Kansas
Nancy SiddensIndependent Language Teaching ConsultantCambridge, Massachusetts
Bonnie SpenceMathematics LecturerMissoula, Montana
Susan Troutman Associate Director for Secondary Programs, RUSMPHouston, Texas
Carolyn White Assoc. Director for Elem. and Int. Programs, RUSMPHouston, Texas
We would also like to thank all of our reviewers who provided feedback during the fi nal development phases. For a complete list of the Big Ideas Math program reviewers, please visit www.BigIdeasLearning.com.
Apply mathematics to problems arising in everyday life, society, and the workplace.
Real-life scenarios are utilized in Explorations, Examples, Exercises, and Assessments so students have opportunities to apply the mathematical concepts they have learned to realistic situations.
Real-world problems help students use the structure of mathematics to break down and solve more diffi cult problems.
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Reasoning, Critical Thinking, Abstract Reasoning, and Problem Solving exercises challenge students to apply their acquired knowledge and reasoning skills to solve each problem.
Students are continually encouraged to evaluate the reasonableness of their solutions and their steps in the problem-solving process.
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Students are provided opportunities for selecting and utilizing the appropriate mathematical tool in Using Tools exercises. Students work with graphing calculators, dynamic geometry software, models, and more.
A variety of tool papers and manipulatives are available for students to use in problems as strategically appropriate.
vi
Texas Mathematical Process Standards
Modeling Real-Life Problems
Modeling with Mathematics
Water fountains are usually designed to give a specifi c visual effect. For example,
the water fountain shown consists of streams of water that are shaped like parabolas.
Notice how the streams are designed to land on the underwater spotlights. Write and
graph a quadratic function that models the path of a stream of water with a maximum
height of 5 feet, represented by a vertex of (3, 5), landing on a spotlight 6 feet from the
water jet, represented by (6, 0).
SOLUTION
1. Understand the Problem You know the vertex and another point on the graph
that represents the parabolic path. You are asked to write and graph a quadratic
function that models the path.
2. Make a Plan Use the given points and the vertex form to write a quadratic
function. Then graph the function.
Monitoring Progress
W
t
N
g
h
w
HSTX_ALG1_PE_08.04.indd 431 3/24/14 1:36 PM
Maintaining Mathematical Proficiency
29. PROBLEM SOLVING The graph shows the percent p (in decimal form) of battery power remaining in a laptop computer after t hours of use. A tablet computer initially has 75% of its battery power remaining and loses 12.5% per hour. Which computer’s battery will last longer? Explain. (See Example 5.)
Laptop Battery
Pow
er r
emai
nin
g(d
ecim
al f
orm
)
00.20.40.60.81.01.2p
Hours20 4 6 t1 3 5
HSTX_Alg1_PE_03.03.indd 112 3/24/14 1:32 PM
USING TOOLS In Exercises 21–26, solve the inequality. Use a graphing calculator to verify your answer.
21. 36 < 3y 22. 17v ≥ 51
≤
≤
≤
≤
Monitoring Progress and Modeling with Mathematics
Vocabulary and Core Concept Check
HSTX_Alg1_PE_02.03.indd 63 3/31/14 5:01 PM
vii
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Students are asked to construct arguments, critique the reasoning of others, and evaluate multiple representations of problems in specialized exercises, including Making an Argument, How Do You See It?, Drawing Conclusions, Reasoning, Error Analysis, Problem Solving, and Writing.
Real-life situations are translated into diagrams, tables, equations, and graphs to help students analyze relationships and draw conclusions.
Create and use representations to organize, record, and communicate mathematical ideas.
Modeling with Mathematics exercises allow students to interpret a problem in the context of a real-life situation, while utilizing tables, graphs, visual representations, and formulas.
Multiple representations are presented to help students move from concrete to representative and into abstract thinking.
Analyze mathematical relationships to connect and communicate mathematical ideas.
Using Structure exercises provide students with the opportunity to explore patterns and structure in mathematics.
Stepped-out Examples encourage students to maintain oversight of their problem-solving process and pay attention to the relevant details in each step.
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Vocabulary and Core Concept Check exercises require students to use clear, precise mathematical language in their solutions and explanations.
Performance Tasks for every chapter allow students to apply their skills to comprehensive problems and utilize precise mathematical language when analyzing, interpreting, and communicating their answers.
38. MODELING WITH MATHEMATICS You start a chain
email and send it to six friends. The next day, each
of your friends forwards the email to six people. The
process continues for a few days.
a. Write a function that
represents the number of
people who have received
the email after n days.
b. After how many days will
1296 people have received
the email?
HSTX_ALG1_PE_06.05.indd 317 3/24/14 1:35 PM
Inequalities with Special Solutions
Solve (a) 8b − 3 > 4(2b + 3) and (b) 2(5w − 1) ≤ 7 + 10w.
SOLUTION
a. 8b − 3 > 4(2b + 3) Write the inequality.
8b − 3 > 8b + 12 Distributive Property
− 8b − 8b Subtract 8b from each side.
−3 > 12 Simplify.
The inequality −3 > 12 is false. So, there is no solution.
Monitoring Progress
HSTX_Alg1_PE_02.04.indd 69 3/24/14 1:31 PM
Core Vocabulary
Core Concepts
Mathematical Thinking
Any BeginningWith so many ways to represent a linear relationship, where do you start? Use what you know to move between equations, graphs, tables, and contexts.
To explore the answer to this question and more, go to BigIdeasMath.com.
Performance Task
HSTX_Alg1_PE_04.EOC.indd 209 3/24/14 1:34 PM
54. HOW DO YOU SEE IT? Consider Squares 1–6 in
the diagram.
124
5
6
3
a. Write a sequence in which each term an is the
side length of square n.
b. What is the name of this sequence? What is the
next term of this sequence?
c. Use the term in part (b) to add another square to
the diagram and extend the spiral.
Maintaining Mathematical Proficiency
HSTX_ALG1_PE_06.06.indd 326 3/31/14 5:05 PM
Maintaining Mathematical Profi ciency ............................................1
Mathematical Thinking ..................................................................2
1.1 Solving Simple EquationsExplorations .................................................................................3Lesson ..........................................................................................4
1.2 Solving Multi-Step EquationsExplorations ...............................................................................11Lesson ........................................................................................12
Study Skills: Completing Homework Effi ciently ........................191.1–1.2 Quiz .............................................................................20
1.3 Solving Equations with Variables on Both Sides Explorations ...............................................................................21 Lesson ........................................................................................22
1.4 Rewriting Equations and Formulas Explorations ...............................................................................27 Lesson ........................................................................................28
Performance Task: Magic of Mathematics ...............................35 Chapter Review ......................................................................36 Chapter Test ............................................................................39 Standards Assessment ..........................................................40
viii
11Solving Linear Equations
See the Big Idea Learn how boat navigators use dead reckoning to calculate their distance covered in a single direction.
ix
22Solving Linear Inequalities Maintaining Mathematical Profi ciency ..........................................43
Mathematical Thinking ................................................................44
2.1 Writing and Graphing Inequalities Explorations ...............................................................................45 Lesson ........................................................................................46
2.2 Solving Inequalities Using Addition or Subtraction Explorations ...............................................................................53 Lesson ........................................................................................54
2.3 Solving Inequalities Using Multiplication or Division Explorations ...............................................................................59 Lesson ........................................................................................60
Study Skills: Analyzing Your Errors ...........................................65 2.1–2.3 Quiz .............................................................................66
2.4 Solving Multi-Step Inequalities Exploration ................................................................................67 Lesson ........................................................................................68
2.5 Solving Compound Inequalities Explorations ...............................................................................73 Lesson ........................................................................................74
Performance Task: Grading Calculations ..................................79 Chapter Review ......................................................................80 Chapter Test ............................................................................83 Standards Assessment ..........................................................84
See the Big Idea Determine how designers decide on the number of electrical circuits needed in a house.
x
33 Graphing Linear Functions Maintaining Mathematical Profi ciency ..........................................87 Mathematical Thinking ................................................................88
3.1 Functions Explorations ...............................................................................89 Lesson ........................................................................................90
3.2 Linear Functions Exploration ................................................................................97 Lesson ........................................................................................98
3.3 Function Notation Explorations .............................................................................107 Lesson ......................................................................................108 Study Skills: Staying Focused during Class ...............................113 3.1–3.3 Quiz ...........................................................................114
3.4 Graphing Linear Equations in Standard Form Explorations .............................................................................115 Lesson ......................................................................................116
3.5 Graphing Linear Equations in Slope-Intercept Form Explorations .............................................................................123 Lesson ......................................................................................124
3.6 Modeling Direct Variation Explorations .............................................................................133 Lesson ......................................................................................134
3.7 Transformations of Graphs of Linear Functions Explorations .............................................................................139 Lesson ......................................................................................140 Performance Task: The Cost of a T-Shirt .................................149 Chapter Review ....................................................................150 Chapter Test ..........................................................................155 Standards Assessment ........................................................156
See the Big Idea Discover why unlike almost any other natural phenomenon, light travels at a constant speed.
xi
44Writing Linear Functions Maintaining Mathematical Profi ciency ........................................159 Mathematical Thinking ..............................................................160
4.1 Writing Equations in Slope-Intercept Form Explorations .............................................................................161 Lesson ......................................................................................162
4.2 Writing Equations in Point-Slope Form Explorations .............................................................................167 Lesson ......................................................................................168
4.3 Writing Equations in Standard Form Explorations .............................................................................173 Lesson ......................................................................................174
4.4 Writing Equations of Parallel and Perpendicular Lines Explorations .............................................................................179 Lesson ......................................................................................180 Study Skills: Getting Actively Involved in Class .........................185 4.1–4.4 Quiz ...........................................................................186
4.5 Scatter Plots and Lines of Fit Explorations .............................................................................187 Lesson ......................................................................................188
4.6 Analyzing Lines of FIt Exploration ..............................................................................193 Lesson ......................................................................................194
4.7 Arithmetic Sequences Exploration ..............................................................................201 Lesson ......................................................................................202 Performance Task: Any Beginning .........................................209 Chapter Review ....................................................................210 Chapter Test ..........................................................................213 Standards Assessment ........................................................214
See the Big Idea Explore wind power and discover where the future of wind power will take us.
xii
55 Solving Systems of Linear Equations Maintaining Mathematical Profi ciency ........................................217 Mathematical Thinking ..............................................................218
5.1 Solving Systems of Linear Equations by GraphingExplorations .............................................................................219Lesson ......................................................................................220
5.2 Solving Systems of Linear Equations by SubstitutionExplorations .............................................................................225Lesson ......................................................................................226
5.3 Solving Systems of Linear Equations by Elimination Explorations .............................................................................231
Lesson ......................................................................................2325.4 Solving Special Systems of Linear Equations
Explorations .............................................................................237Lesson ......................................................................................238Study Skills: Analyzing Your Errors .........................................243
5.1–5.4 Quiz ...........................................................................244
5.5 Solving Equations by Graphing Explorations .............................................................................245
Lesson ......................................................................................246 5.6 Linear Inequalities in Two Variables
Explorations .............................................................................251Lesson ......................................................................................252
5.7 Systems of Linear Inequalities Explorations .............................................................................259
Lesson ......................................................................................260 Performance Task: Prize Patrol ..............................................267 Chapter Review ....................................................................268 Chapter Test ..........................................................................271 Standards Assessment ........................................................272
See the Big Idea Learn how fi sheries manage their complex ecosystems.
xiii
66Exponential Functions and Sequences Maintaining Mathematical Profi ciency ........................................275 Mathematical Thinking ..............................................................276
6.1 Properties of Exponents Exploration ..............................................................................277 Lesson ......................................................................................278
6.2 Radicals and Rational Exponents Explorations .............................................................................285 Lesson ......................................................................................286
6.3 Exponential Functions Explorations .............................................................................291 Lesson ......................................................................................292
6.4 Exponential Growth and Decay Explorations .............................................................................299 Lesson ......................................................................................300
Study Skills: Analyzing Your Errors .........................................309 6.1–6.4 Quiz ...........................................................................310
6.5 Geometric Sequences Explorations .............................................................................311 Lesson ......................................................................................312
6.6 Recursively Defi ned Sequences Explorations .............................................................................319 Lesson ......................................................................................320
Performance Task: The New Car ............................................327 Chapter Review ....................................................................328 Chapter Test ..........................................................................331 Standards Assessment ........................................................332
See the Big Idea Explore the variety of recursive sequences in language, art, music, nature, and games.
xiv
77 Polynomial Equations and Factoring Maintaining Mathematical Profi ciency ........................................335 Mathematical Thinking ...............................................................336
7.1 Adding and Subtracting PolynomialsExplorations .............................................................................337Lesson .......................................................................................338
7.2 Multiplying PolynomialsExplorations .............................................................................345Lesson .......................................................................................346
7.3 Special Products of Polynomials Explorations .............................................................................351
Lesson .......................................................................................3527.4 Dividing Polynomials
Explorations .............................................................................357Lesson .......................................................................................358
7.5 Solving Polynomial Equations in Factored Form Explorations .............................................................................363
Lesson .......................................................................................364Study Skills: Preparing for a Test .............................................369
7.1–7.5 Quiz ...........................................................................370
7.6 Factoring x2 + bx + cExploration ...............................................................................371Lesson .......................................................................................372
7.7 Factoring ax2 + bx + cExploration ...............................................................................377Lesson .......................................................................................378
7.8 Factoring Special Products Explorations .............................................................................383
Lesson .......................................................................................384 7.9 Factoring Polynomials Completely
Explorations .............................................................................389Lesson .......................................................................................390
Performance Task: The View Matters .....................................395 Chapter Review ....................................................................396 Chapter Test ...........................................................................399 Standards Assessment ........................................................400
See the Big Idea Explore whether seagulls and crows use the optimal height while dropping hard-shelled food to crack it open.
xv
88Graphing Quadratic Functions Maintaining Mathematical Profi ciency ........................................403
Mathematical Thinking ..............................................................404
8.1 Graphing f(x) = ax2
Exploration ..............................................................................405 Lesson ......................................................................................406
8.2 Graphing f(x) = ax2 + c Explorations .............................................................................411 Lesson ......................................................................................412
8.3 Graphing f(x) = ax2 + bx + c Explorations .............................................................................417 Lesson ......................................................................................418
Study Skills: Learning Visually ................................................425 8.1–8.3 Quiz ...........................................................................426
8.4 Graphing f(x) = a(x − h)2 + k Explorations .............................................................................427 Lesson ......................................................................................428
8.5 Using Intercept Form Exploration ..............................................................................435 Lesson ......................................................................................436
8.6 Comparing Linear, Exponential, and Quadratic Functions Explorations .............................................................................445 Lesson ......................................................................................446
Performance Task: Asteroid Aim ...........................................455 Chapter Review ....................................................................456 Chapter Test ..........................................................................459 Standards Assessment ........................................................460
See the Big Idea Investigate the link between population growth and the classic exponential pay doubling application.
xvi
99 Solving Quadratic Equations Maintaining Mathematical Profi ciency ........................................463
Mathematical Thinking ..............................................................464
9.1 Properties of RadicalsExplorations .............................................................................465Lesson ......................................................................................466
9.2 Solving Quadratic Equations by GraphingExplorations .............................................................................475Lesson ......................................................................................476
9.3 Solving Quadratic Equations Using Square Roots Explorations .............................................................................485
Lesson ......................................................................................486Study Skills: Keeping a Positive Attitude .................................491
9.1–9.3 Quiz ...........................................................................492
9.4 Solving Quadratic Equations by Completing the Square Explorations .............................................................................493
Lesson ......................................................................................494 9.5 Solving Quadratic Equations Using the
Quadratic Formula Explorations .............................................................................503
Lesson ......................................................................................504 Performance Task: Form Matters ...........................................513 Chapter Review ....................................................................514 Chapter Test ..........................................................................517 Standards Assessment ........................................................518
Selected Answers ............................................................ A1 English-Spanish Glossary .............................................. A43
Index ............................................................................... A53Reference ....................................................................... A61
See the Big Idea Explore the Parthenon and investigate how the use of the golden rectangle has evolved since its discovery.
xvii
Get ready for each chapter by Maintaining Mathematical ProficiencyMaintaining Mathematical Proficiency and sharpening your
Mathematical ThinkingMathematical Thinking . Begin each section by working through the
to Communicate Your AnswerCommunicate Your Answer to the Essential QuestionEssential Question. Each Lesson will explain
What You Will LearnWhat You Will Learn through , Core Core ConceptsConcepts , and Core VocabularyCore Vocabullarry .
Answer the Monitoring ProgressMonitoring Progress questions as you work through each lesson. Look for
STUDY TIPS, COMMON ERRORS, and suggestions for looking at a problem ANOTHER WAY
throughout the lessons. We will also provide you with guidance for accurate mathematical READING
and concept details you should REMEMBER.
Sharpen your newly acquired skills with Exercises at the end of every section. Halfway through
each chapter you will be asked What Did You Learn? and you can use the Mid-Chapter Quiz
to check your progress. You can also use the Chapter Review and Chapter Test to review and
assess yourself after you have completed a chapter.
Apply what you learned in each chapter to a Performance Task and build your confi dence for
taking standardized tests with each chapter’s Standards Assessment .
For extra practice in any chapter, use your Online Resources, Skills Review Handbook, or your
Student Journal.
How to Use Your Math Book
