BIG IDEAS
M AT H
®
TEXAS EDITION
Ron Larson and Laurie Boswell
Erie, Pennsylvania
BigIdeasLearning.com
Big Ideas Learning, LLC
1762 Norcross Road
Erie, PA 16510-3838
USA
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at 1-877-552-7766 or visit us at BigIdeasLearning.com.
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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
Authors
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.
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.
iii
For the Student
Welcome to Big Ideas Math Algebra 1. From start to finish, 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.
Graphing Quadratic
Functions
8
Maintaining Mathematical Proficiency
Graphing Linear Equations
ax 2
Graphing f (x) =
Graphing f (x) = ax 2 + c
Graphing f (x) = ax 2 + bx + c
Graphing f (x) = a(x − h)2 + k
Using Intercept Form
Comparing Linear, Exponential, and Quadratic Functions
8.1
8.2
8.3
8.4
8.5
8.6
(A.3.C)
Graph y = −x − 1.
Example 1
Step 1 Make a table of values.
SEE the Big Idea
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.
2
(−1, 0)
(0, −1)
−4
Graph the linear equation.
1. y = 2x − 3
Town Population
Populati
l ion ((p.
p 450)
450))
2
x
(1, −2)
(2, −3)
2. y = −3x + 4
1
3. y = −—2 x − 2
4. y = x + 5
Evaluating Expressions
Satellite Dish (p
(p. 443)
y
y = −x − 1
Step 3 Draw a line through the points.
(A.11.B)
Evaluate 2x2 + 3x − 5 when x = −1.
Example 2
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.
8.1
= −6
Mathematically
proficient students use aSubtract.
problem-solving model that
incorporates analyzing given information, formulating a plan or strategy,
determining
a solution,
justifying the solution, and evaluating the
expression
when
x = −2.
problem-solving process and the reasonableness of the solution. (A.1.B)
6. 3x 2 + x − 2
Mathematical
Evaluate the
Thinking
Roller Coaster (p. 434)
5. 5x 2 − 9
Problem-Solving
Strategies
7. −x 2 + 4x + 1
TEXAS ESSENTIAL
KNOWLEDGE AND SKILLS
A.6.A
A.7.A
A.7.C
8. x 2 + 8x + 5
Core Concept
9. −2x 2 − 4x + 3
10. −4x 2 + 2x − 6
ABSTRACT
REASONING Complete the table. Find a pattern in the differences of
Trying11.Special
Cases
consecutive y-values. Use the pattern to write an expression for y when x = 6.
When solving a problem in mathematics, it can be helpful to try special cases of the
original problem. For instance,
you
a quadratic
x in this chapter,
1
2 will
3 learn
4 to graph
5
function of the form f (x) = ax2 + bx + c. The problem-solving strategy used is to
= the
ax 2form f (x) = ax2. From there, you progress to
first graph quadratic functionsy of
other forms of quadratic functions.
Firework Explosion (p
(p. 423)
Garden
Waterfalls
Ga
G
arden
den W
ater
at
erffall
llss ((p.
ll
p. 416)
416)
Mathematical Thinking: Mathematically proficient students can apply the mathematics they know to solve problems
arising in everyday life, society, and the workplace.
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
Graphing f (x) = ax2
Essential Question
What are some of the characteristics of the
graph of a quadratic function of the form f (x) = ax 2?
Graphing Quadratic Functions
Work with a partner. Graph each quadratic function. Compare each graph to the
graph of f (x) = x2.
a. g(x) =
b. g(x) = −5x2
3x2
y
y
10
4
8
40
−6
−4
2
4
−8
f(x) = x 2
−2
2
4
f(x) = x 2
−2
−4
2
−6
−4
6
4
6x
−12
−16
6x
Graphing the Parent Quadratic Function
Graph the parent quadratic function y =
x2.
Then describe its graph.
SOLUTION
6
The function is of the form y = ax 2, where a = 1. By plotting several points, you can see
that the graph is U-shaped, as shown.
4
8
a = 1
• When 0 < ∣ a ∣ < 1, the graph of f (x) = (ax)2
is a horizontal stretch of the graph of
f (x) = x2.
y
0 < a < 1
(
)
1
(
n(x) = − 14 x
f(x) = x 2
)
3.
(
1
)
2
−2
Step 1 Make a table of values.
x
n(x)
Step 2 Plot the ordered pairs.
16
y
1 −x2
1. y =
1 2
=—
x
16
24
5. f(
f (x)
x) =
−16
−8
0
8
16
16
4
0
4
16
−2
8
−8
8
404
−2
−1
y
y=
1
(0, 0)
1 2
x
4
(2, 1)
2
x
+ 4x + 3
Chapter 8
6. f(
f (x)
x) =
8
SOLUTION
4
width
−8
−4
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.
−450 −350 −250
8 x
5. g(x) = 6x2
Help in English and Spanish at BigIdeasMath.com
3. g(x) = 5x2
4. h(x) = —3 x2
5. p(x) = −3x2
6. q(x) = −0.1x2
7. n(x) = (3x)2
8. g(x) = −—2 x
(
1
)
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.
−50
y
50
250 350 450
x
−250
In Exercises 5–16, graph the function. Compare the
graph to the graph of f (x) = x2. (See Examples 2, 3,
and 4.)
Graph the function. Compare the graph to the graph of f (x) = x2.
−4
−2
2
4
6
6x
6. b(x) = 2.5x2
8. j(x) = 0.75x2
9
9. m(x) = −2x2
10. q(x) = −—2 x2
−350
19. PROBLEM SOLVING The breaking strength z
(in pounds) of a manila rope can be modeled by
z = 8900d 2, where d is the diameter (in inches)
of the rope.
d
11. k(x) = −0.2x2
12. p(x) = −—3 x2
a. Describe the domain and
range of the function.
13. n(x) = (2x)2
14. d(x) = (−4x)2
b. Graph the function using
the domain in part (a).
16. r(x) = (0.1x)2
c. A manila rope has four times the breaking strength
of another manila rope. Does the stronger rope
have four times the diameter? Explain.
(
1
15. c(x) = −—3 x
)
2
2
Section 8.1
Graphing f(x) = ax 2
409
f(x) = x 2
4
−2
2
−4
−6
−6
−4
−2
2
4
6x
REASONING
To be proficient in math,
you need to make sense
of quantities and their
relationships in
problem situations.
Communicate 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 figure shows the graph of a quadratic function
7
of the form y = ax2. Which of the intervals
in Question 3 describes the value of a? Explain
your reasoning.
−6
6
−1
Section 8.1
−150
1
1
8. y = −2(x − 1)2 + 1
a bridge can be modeled by y = −0.0012x 2, where x
and y are measured in feet. Find the height and width
of the arch. (See Example 5.)
4
7. h(x) = —4 x2
iv
7. y = −2(x + 1)2 + 1
18. MODELING WITH MATHEMATICS The arch support of
So, the satellite dish is 4 meters wide and 1 meter deep.
Graphing Quadratic Functions
− 4x + 3
depth
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.
Chapter 8
2
y4.= 0.5x
f (x)
f(
x) = 2x
2 2−1
y
50
Use the domain of the function to find the width
of the dish. Use the range to find 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.
408
✗
3. f(
f (x)
x) = 22x 2 + 1
Graphing Quadratic Functions
12
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.
Monitoring Progress
1
—2 x 2
y
Solving a Real-Life Problem
2
x
x
4.
(−2, 1)
graphing and comparing y = x2 and y = 0.5x2.
2. y = 2x
2 2
4
−6
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.
16 x
1 2
—2 x 2
f(x) = x 2
9. How are the graphs in Monitoring Progress Questions 1−8 similar? How
2 they different?
y = xare
Step 3 Draw a smooth curve through the points.
−16
17. ERROR ANALYSIS Describe and correct the error in
In Exercises 3 and 4, identify characteristics of the
quadratic function and its graph. (See Example 1.)
2
SOLUTION
Rewrite n. n(x) = −—4 x
FINALpages
2. WRITING When does the graph of a quadratic function open up? open down?
Monitoring Progress and Modeling with Mathematics
(ax)2
Graph n(x) = −—4 x . Compare the graph to the graph of f (x) = x2.
2
2
1. VOCABULARY What is the U-shaped graph of a quadratic function called?
x
y
−6
6
4
Vocabulary and Core Concept Check
horizontal shrink of the graph of f (x) = x2.
32
8 Tutorial Help in English and Spanish at BigIdeasMath.com
a > 1
• When ∣ a ∣ > 1, the graph of f (x) = (ax)2 is a
Graphing y =
10
HSTX_ALG1_PE_08.OP • March19,20141:44PM
Graphing f (x) = (ax)2
y
10
Exercises
8.1
y
2
y
Core Concept
1 2
d. g(x) = —
x
10
c. g(x) = −0.2x2
Graphing f(x) = ax 2
405
Big Ideas Math
High School Research
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 Mathematics
National Research Council ©2001
Curriculum Focal Points and the Principles and Standards for School Mathematics ©2000
National Council of Teachers of Mathematics (NCTM)
Project Based Learning
The Buck Institute
Rigor/Relevance FrameworkTM
International Center for Leadership in Education
Universal Design for Learning Guidelines
CAST ©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.
Carolyn Briles
Mathematics Teacher
Leesburg, Virginia
Melissa Ruffin
Master of Education
Austin, Texas
Jean Carwin
Math Specialist/TOSA
Snohomish, Washington
Connie Schrock, Ph.D.
Mathematics Professor
Emporia, Kansas
Alice Fisher
Instructional Support Specialist, RUSMP
Houston, Texas
Nancy Siddens
Independent Language Teaching Consultant
Cambridge, Massachusetts
Kristen Karbon
Curriculum and Assessment Coordinator
Troy, Michigan
Bonnie Spence
Mathematics Lecturer
Missoula, Montana
Anne Papakonstantinou, Ed.D.
Project Director, RUSMP
Houston, Texas
Susan Troutman
Associate Director for Secondary Programs, RUSMP
Houston, Texas
Richard Parr
Executive Director, RUSMP
Houston, Texas
Carolyn White
Assoc. Director for Elem. and Int. Programs, RUSMP
Houston, Texas
We would also like to thank all of our reviewers who provided feedback during the final
development phases. For a complete list of the Big Ideas Math program reviewers, please visit
www.BigIdeasLearning.com.
v
Texas Mathematical
Process Standards
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 difficult problems.
Modeling Real-Life Problems
Vocabulary and Core Concept Check
Modeling with Mathematics
W
Water
fountains are usually designed to give a specific visual effect. For example,
tthe 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
N
ggraph a quadratic function that models the path of a stream of water with a maximum
hheight of 5 feet, represented by a vertex of (3, 5), landing on a spotlight 6 feet from the
water jet, represented by (6, 0).
w
Monitoring Progress and Modeling with Mathematic
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.
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.
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
Power remaining
(decimal form)
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.
p
1.2
1.0
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5 6 t
Hours
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
USING TOOLS In Exercises 21–26, solve the inequality.
Monitoring Progress
Use a graphing calculator to verify your answer.
and utilizing the appropriate mathematical
tool in
21. 36 < 3y
22. 17v ≥ 51
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.
HSTX_ALG1_PE_08.04.indd 431
vi
3/24/14 1:36 PM
HSTX_Alg1_PE_02.03.indd 63
54. HOW DO YOU SEE IT? Consider Squares 1– 6 in
Communicate mathematical ideas, reasoning, and their
implications using multiple representations, including
symbols, diagrams, graphs, and language as appropriate.
the diagram.
5
6
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.
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.
2 1
3
4
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
Create and use representations to organize, record,
and communicate mathematical ideas.
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?
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.
Core Vocabulary
Multiple representations are presented to help
students move from concrete to representative
and into abstract thinking.
HSTX_ALG1_PE_06.06.indd 326
Core Concepts
Analyze mathematical relationships to connect and
communicate mathematical ideas.
Inequalities with Special Solutions
Solve (a) 8b − 3 > 4(2b + 3) and (b) 2(5w − 1) ≤ 7 + 10w.
Using Structure exercises provide students with
the opportunity to explore patterns and
SOLUTION
a. 8b − 3 > 4(2b + 3)
Write the inequality.
structure in mathematics.
8b − 3 > 8b + 12
Distributive Property
Stepped-out Examples encourage students to
− 8b
− 8b
Subtract 8b from each side.
maintain oversight of their problem-solving
−3 > 12 Simplify.
process and pay attention to the relevant
Mathematical Thinking
The inequality −3 > 12 is false. So, there is no solution.
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.
Performance Task
Monitoring Progress
Any Beginning
With 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.
HSTX_Alg1_PE_02.04.indd 69
HSTX_Alg1_PE_04.EOC.indd 209
3/24/14 1:31 PM
vii
3/24/14 1:34 PM
1
Solving Linear Equations
Maintaining Mathematical Proficiency ............................................1
Mathematical Thinking ..................................................................2
1.1
Solving Simple Equations
Explorations .................................................................................3
Lesson ..........................................................................................4
1.2
Solving Multi-Step Equations
Explorations ...............................................................................11
Lesson ........................................................................................12
Study Skills: Completing Homework Efficiently ........................19
1.1–1.2 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
See the Big Idea
Learn how boat navigators use dead
reckoning to calculate their distance covered
in a single direction.
viii
Solving Linear Inequalities
2
Maintaining Mathematical Proficiency ..........................................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.
ix
3
Graphing Linear Functions
Maintaining Mathematical Proficiency ..........................................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.
x
Writing Linear Functions
4
Maintaining Mathematical Proficiency ........................................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.
xi
5
Solving Systems of Linear Equations
Maintaining Mathematical Proficiency ........................................217
Mathematical Thinking ..............................................................218
5.1
Solving Systems of Linear Equations by Graphing
Explorations .............................................................................219
Lesson ......................................................................................220
5.2
Solving Systems of Linear Equations by Substitution
Explorations .............................................................................225
Lesson ......................................................................................226
5.3
Solving Systems of Linear Equations by Elimination
Explorations .............................................................................231
Lesson ......................................................................................232
5.4
Solving Special Systems of Linear Equations
Explorations .............................................................................237
Lesson ......................................................................................238
Study 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 .............................................................................251
Lesson ......................................................................................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 fisheries manage their complex
ecosystems.
xii
Exponential Functions and Sequences
6
Maintaining Mathematical Proficiency ........................................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
6.5
Study Skills: Analyzing Your Errors .........................................309
6.1–6.4 Quiz ...........................................................................310
Geometric Sequences
Explorations .............................................................................311
Lesson ......................................................................................312
6.6
Recursively Defined 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.
xiii
7
Polynomial Equations and Factoring
Maintaining Mathematical Proficiency ........................................335
Mathematical Thinking ...............................................................336
7.1
Adding and Subtracting Polynomials
Explorations .............................................................................337
Lesson .......................................................................................338
7.2
Multiplying Polynomials
Explorations .............................................................................345
Lesson .......................................................................................346
7.3
Special Products of Polynomials
Explorations .............................................................................351
Lesson .......................................................................................352
7.4
Dividing Polynomials
Explorations .............................................................................357
Lesson .......................................................................................358
7.5
Solving Polynomial Equations in Factored Form
Explorations .............................................................................363
Lesson .......................................................................................364
Study Skills: Preparing for a Test .............................................369
7.1–7.5 Quiz ...........................................................................370
7.6
Factoring x 2 + bx + c
Exploration...............................................................................371
Lesson .......................................................................................372
7.7
Factoring ax 2 + bx + c
Exploration...............................................................................377
Lesson .......................................................................................378
7.8
Factoring Special Products
Explorations .............................................................................383
Lesson .......................................................................................384
7.9
Factoring Polynomials Completely
Explorations .............................................................................389
Lesson .......................................................................................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.
xiv
Graphing Quadratic Functions
8
Maintaining Mathematical Proficiency ........................................403
Mathematical Thinking ..............................................................404
8.1
Graphing f(x) = ax 2
Exploration ..............................................................................405
Lesson ......................................................................................406
8.2
Graphing f(x) = ax 2 + c
Explorations .............................................................................411
Lesson ......................................................................................412
8.3
Graphing f(x) = ax 2 + 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.
xv
9
Solving Quadratic Equations
Maintaining Mathematical Proficiency ........................................463
Mathematical Thinking ..............................................................464
9.1
Properties of Radicals
Explorations .............................................................................465
Lesson ......................................................................................466
9.2
Solving Quadratic Equations by Graphing
Explorations .............................................................................475
Lesson ......................................................................................476
9.3
Solving Quadratic Equations Using Square Roots
Explorations .............................................................................485
Lesson ......................................................................................486
Study 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 ............................................................................... A53
Reference ....................................................................... A61
See the Big Idea
Explore the Parthenon and investigate how
the use of the golden rectangle has evolved
since its discovery.
xvi
How to Use Your
Math Book
Get ready for each chapter by
Maintaining Mathematical Proficiency and sharpening your
Mathematical Thinking . Begin each section by working through the
Communicate Your Answer to the Essential Question. Each Lesson will explain
,
Vocabulary
larry
Core Concepts , and Core Vocabul
What You Will Learn through
Answer the Monitoring Progress questions as you work through each lesson. Look for
to
.
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
each chapter you will be asked
Exercises at the end of every section. Halfway through
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
taking standardized tests with each chapter’s
Task and build your confidence for
Standards Assessment .
For extra practice in any chapter, use your Online Resources, Skills Review Handbook, or your
Student Journal.
xvii