i
connectED.mcgraw-hill.comccccc Your Digital Math Portal
Preparing for Preparing for Advanced AlgebraAdvanced Algebra
Personal Tutor
p. P6Multilingual
eGlossary
p. P2
Vocabulary
p. P4Foldables
p. P2
Table of ContentsEd
Fre
eman
/Sto
ne/G
etty
Imag
es
Get Started On Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3
0-1 Representing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P4
0-2 FOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P6
0-3 Factoring Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P7
0-4 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P9
0-5 Adding Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P13
0-6 Multiplying Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P16
0-7 Congruent and Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P20
0-8 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P22
0-9 Measures of Center, Spread, and Position . . . . . . . . . . . . . . . . . . . . . . . . .P24
Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P29
Preparing for Advanced Algebra
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Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 1 | Linear Relations and Functions
Personal Tutor
pp. 6, 63Multilingual
eGlossary
pp. 4, 60
Vocabulary
pp. 5, 69Animation
pp. 12, 84
Equations and Equations and InequalitiesInequalities
Jon Boyes/Photographer’s Choice/Getty Images
Equations and Inequalities
Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1-1 Expressions and Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1-2 Properties of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
1-3 Solving Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
1-4 Solving Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
1-5 Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Explore: Algebra Lab Interval Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1-6 Solving Compound and Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . .41
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Standardized Test Practice, Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
A.SSE.1.a, A.SSE.1.b
A.SSE.2
A.CED.1
A.SSE.1.b, A.CED.1
A.CED.1, A.CED.3
A.CED.1, A.CED.3
MathematicalContent
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iii iii
Unit 1 | Linear Relations and Functions
Self-Check
Practice
pp. 7, 127
Foldables
pp. 4, 60Graphing
Calculator
p. 90
Virtual
Manipulatives
pp. 28, 61
Linear Relations Linear Relations and Functionsand Functions
Roin
e M
agnu
sson
/Pho
todi
sc/G
etty
Imag
es
Linear Relations and Functions
Get Ready for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2-1 Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
Extend: Algebra Lab Discrete and Continuous Functions . . . . . . . . . . . . . . . . . . . . . . . 68
2-2 Linear Relations and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Extend: Algebra Lab Roots of Equations and Zeros of Functions . . . . . . . . . . . . . . . . . . 75
2-3 Rate of Change and Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
2-4 Writing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Extend: Graphing Technology Lab Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
2-5 Scatter Plots and Lines of Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92
Extend: Algebra Lab Correlation and Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2-6 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
Explore: Graphing Technology Lab Families of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . 108
2-7 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
2-8 Graphing Linear and Absolute Value Inequalities. . . . . . . . . . . . . . . . . . . . . .117
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128
Standardized Test Practice, Chapters 1–2 . . . . . . . . . . . . . . . . . . . . . . . . . .130
F.IF.4, F.IF.5
F.IF.4
F.IF.4, F.IF.9
F.IF.4
F.IF.4, F.IF.6
A.SSE.1.b, A.CED.2
F.IF.4
F.IF.4
F.IF.4
F.IF.4, F.IF.7.b
F.BF.3
F.IF.4, F.BF.3
A.CED.3
MathematicalContent
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Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 1 | Linear Relations and Functions
Personal Tutor
pp. 136, 222Multilingual
eGlossary
pp. 134, 218
Vocabulary
pp. 206, 290Animation
pp. 146, 247
Systems of Equations Systems of Equations and Inequalitiesand Inequalities
DreamPictures/Blend Im
ages/Getty Images
Systems of Equations and Inequalities
Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Explore: Graphing Technology Lab Intersections of Graphs . . . . . . . . . . . . . . . . . . . . . 135
3-1 Solving Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
3-2 Solving Systems of Inequalities by Graphing . . . . . . . . . . . . . . . . . . . . . . . . .146
Extend: Graphing Technology Lab Systems of Linear Inequalities . . . . . . . . . . . . . . . . 153
3-3 Optimization with Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154
3-4 Systems of Equations in Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . .161
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168
Explore: Spreadsheet Lab Organizing Data with Matrices. . . . . . . . . . . . . . . . . . . . . . 169
3-5 Operations with Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171
3-6 Multiplying Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179
Extend: Graphing Technology Lab Operations with Matrices . . . . . . . . . . . . . . . . . . . 187
3-7 Solving Systems of Equations Using Cramer’s Rule . . . . . . . . . . . . . . . . . . . .189
3-8 Solving Systems of Equations Using Inverse Matrices. . . . . . . . . . . . . . . . . .198
Extend: Graphing Technology Lab Augmented Matrices . . . . . . . . . . . . . . . . . . . . . . . 205
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212
Standardized Test Practice, Chapters 1–3 . . . . . . . . . . . . . . . . . . . . . . . . . .214
A.CED.3, A.REI.11
A.CED.3
A.CED.3
A.CED.3
A.CED.3
A.CED.3
MathematicalContent
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Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations
Quadratic Functions Quadratic Functions and Relationsand Relations
Virtual
Manipulatives
pp. 137, 219
Graphing
Calculator
pp. 205, 237
Foldables
pp. 134, 218Self-Check
Practice
pp. 183, 295
Blac
k 10
0/Al
lspo
rt Co
ncep
ts/G
etty
Imag
es
Get Ready for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
4-1 Graphing Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219
Extend: Graphing Technology Lab Modeling Real-World Data . . . . . . . . . . . . . . . . . . . 228
4-2 Solving Quadratic Equations by Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . .229
Extend: Graphing Technology Lab Solving Quadratic Equations by Graphing . . . . . . . . 237
4-3 Solving Quadratic Equations by Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . .238
4-4 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246
Extend: Algebra Lab The Complex Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255
4-5 Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256
Extend: Graphing Technology Lab Solving Quadratic Equations. . . . . . . . . . . . . . . . . . 263
4-6 The Quadratic Formula and the Discriminant . . . . . . . . . . . . . . . . . . . . . . . . .264
Explore: Graphing Technology Lab Families of Parabolas . . . . . . . . . . . . . . . . . . . . . . 273
4-7 Transformations of Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275
Extend: Algebra Lab Quadratics and Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . 281
4-8 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .282
Extend: Graphing Technology Lab Modeling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .295
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296
Standardized Test Practice, Chapters 1–4 . . . . . . . . . . . . . . . . . . . . . . . . . .298
Quadratic Functions and Relations
A.SSE.1.a, F.IF.9
F.IF.4
A.CED.2, F.IF.4
A.REI.11
A.SSE.2, F.IF.8.a
N.CN.1, N.CN.2
N.CN.7, F.IF.8.a
N.CN.7
N.CN.7, A.SSE.1.b
F.IF.4, F.BF.3
F.IF.8.a, F.BF.3
F.IF.4, F.IF.6
A.CED.1, A.CED.3
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Unit 1 | Foundations for Functions
Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations
Personal Tutor
pp. 304, 386Multilingual
eGlossary
pp. 302, 384
Vocabulary
pp. 303, 400Animation
pp. 306, 387
Polynomials and Polynomial Functions5PPPPPP5PP
Photodisc/Getty Images
Polynomials and Polynomial Functions
Get Ready for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
5-1 Operations with Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303
Extend: Algebra Lab Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
5-2 Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311
Extend: Graphing Technology Lab Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . 318
Explore: Graphing Technology Lab Power Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 320
5-3 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322
5-4 Analyzing Graphs of Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . .330
Extend: Graphing Technology Lab Modeling Data Using Polynomial Functions . . . . . . 338
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .340
Explore: Graphing Technology Lab Solving Polynomial Equations by Graphing . . . . . . 341
5-5 Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342
Extend: Graphing Technology Lab Polynomial Identities . . . . . . . . . . . . . . . . . . . . . . . 350
5-6 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .352
5-7 Roots and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358
Extend: Graphing Technology Lab Analyzing Polynomial Functions . . . . . . . . . . . . . . . 366
5-8 Rational Zero Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .367
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .373
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .377
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .378
Standardized Test Practice, Chapters 1–5 . . . . . . . . . . . . . . . . . . . . . . . . . .380
A.APR.1
A.APR.6
A.APR.6
F.IF.4
F.IF.4, F.IF.7.c
F.IF.4, F.IF.7.c
F.IF.4, F.IF.7.c
A.CED.1
A.REI.11
A.APR.2, F.IF.7.c
N.CN.9, A.APR.3
A.APR.4
MathematicalContent
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vii vii
Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations
Self-Check
Practice
pp. 326, 443
Foldables
pp. 302, 384Graphing
Calculator
pp. 338, 436
Virtual
Manipulatives
p. 331
Inverses and Radical Functions and Relations6III6FF
Stoc
kbyt
e/Ge
tty Im
ages
Inverses and Radical Functions and Relations
Get Ready for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
6-1 Operations on Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .385
6-2 Inverse Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .393
Extend: Graphing Technology Lab Inverse Functions and Relations. . . . . . . . . . . . . . . 399
6-3 Square Root Functions and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .400
6-4 nth Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .407
Extend: Graphing Technology Lab Graphing nth Root Functions . . . . . . . . . . . . . . . . . 413
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414
6-5 Operations with Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415
6-6 Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422
6-7 Solving Radical Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . .429
Extend: Graphing Technology Lab Solving Radical Equations and Inequalities . . . . . . . 436
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .438
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .444
Standardized Test Practice, Chapters 1–6 . . . . . . . . . . . . . . . . . . . . . . . . . .446
F.IF.9, F.BF.1.b
F.IF.4, F.BF.4.a
F.IF.7.b, F.BF.3
A.SSE.2
F.IF.7.b, F.BF.3
A.SSE.2
A.REI.2
A.REI.2, A.REI.11
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Unit 1 | Foundations for Functions
Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 3 | Advanced Functions and Relations
Personal Tutor
pp. 455, 531Multilingual
eGlossary
pp. 450, 528
Vocabulary
pp. 517, 581Animation
pp. 453, 532
Exponential and Exponential and Logarithmic Functions Logarithmic Functions and Relationsand Relations
Purestock/Getty Images
Exponential and Logarithmic Functions and Relations
Get Ready for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
7-1 Graphing Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .451
Explore: Graphing Technology Lab Solving Exponential Equations and Inequalities . . . 459
7-2 Solving Exponential Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . .461
7-3 Logarithms and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .468
Extend: Graphing Technology Lab Choosing the Best Model . . . . . . . . . . . . . . . . . . . . 476
7-4 Solving Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . .478
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .484
7-5 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .485
7-6 Common Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .492
Extend: Graphing Technology Lab Solving Logarithmic Equations and Inequalities . . . 499
7-7 Base e and Natural Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .501
Explore: Spreadsheet Lab Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
7-8 Using Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . .509
Extend: Graphing Technology Lab Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .517
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .521
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .522
Standardized Test Practice, Chapters 1–7 . . . . . . . . . . . . . . . . . . . . . . . . . .524
F.IF.7.e, F.IF.8.b
A.REI.11
A.CED.1, F.LE.4
F.IF.7.e, F.BF.3
A.SSE.2, A.CED.1
A.CED.1
A.CED.1
A.REI.11
A.SSE.2
F.IF.8.b, F.LE.4
F.BF.1.b
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ix ix
Unit 3 | Advanced Functions and Relations
Self-Check
Practice
pp. 464, 585
Foldables
pp. 450, 528Graphing
Calculator
pp. 516, 579
Virtual
Manipulatives
pp. 451, 557
Rational Functions Rational Functions and Relationsand Relations
Imag
e So
urce
/Mas
terfi
le
Rational Functions and Relations
Get Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
8-1 Multiplying and Dividing Rational Expressions . . . . . . . . . . . . . . . . . . . . . . .529
8-2 Adding and Subtracting Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . .538
8-3 Graphing Reciprocal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .545
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .552
8-4 Graphing Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .553
Extend: Graphing Technology Lab Graphing Rational Functions . . . . . . . . . . . . . . . . . 561
8-5 Variation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .562
8-6 Solving Rational Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . .570
Extend: Graphing Technology Lab Solving Rational Equations and Inequalities . . . . . . 579
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .581
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .585
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .586
Standardized Test Practice, Chapters 1–8 . . . . . . . . . . . . . . . . . . . . . . . . . .588
A.APR.7
A.APR.7
A.CED.2, F.BF.3
A.CED.2, F.IF.9
A.CED.2
A.CED.1, A.REI.2
A.REI.2, A.REI.11
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x x
Unit 1 | Foundations for Functions
Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Unit 3 | Advanced Functions and Relations
Personal Tutor
pp. 600, 660Multilingual
eGlossary
pp. 592, 658
Vocabulary
pp. 599, 710Animation
pp. 641, 659
Conic SectionsConic Sections
Brand X Pictures/PunchStock
Conic Sections
Get Ready for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
9-1 Midpoint and Distance Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .593
9-2 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .599
Explore: Graphing Technology Lab Equations of Circles . . . . . . . . . . . . . . . . . . . . . 606
9-3 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .607
Explore: Algebra Lab Investigating Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
9-4 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .615
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .623
9-5 Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .624
9-6 Identifying Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .632
Extend: Graphing Technology Lab Analyzing Quadratic Relations . . . . . . . . . . . . . . 637
Explore: Graphing Technology Lab Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . 639
9-7 Solving Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .640
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .646
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .651
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .652
Standardized Test Practice, Chapters 1–9 . . . . . . . . . . . . . . . . . . . . . . . .654
A.CED.4
A.SSE.1.b, A.CED.2
A.SSE.1.b, A.CED.4
A.SSE.1.b, A.CED.2
A.SSE.1.b, A.CED.2
A.SSE.1.b, F.IF.9
A.REI.11
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xi xi
Unit 4 | Discrete Mathematics
Self-Check
Practice
pp. 603, 715
Foldables
pp. 592, 658Graphing
Calculator
pp. 639, 690
Virtual
Manipulatives
pp. 594, 681
Sequences and Sequences and SeriesSeries
Mar
tin C
hild
/Pho
todi
sc/G
etty
Imag
es
Sequences and Series
Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
10-1 Sequences as Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .659
10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .666
10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .674
Explore: Algebra Lab Area Under a Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
10-4 Infinite Geometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .683
Extend: Graphing Technology Lab Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .691
10-5 Recursion and Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .692
Extend: Spreadsheet Lab Amortizing Loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698
10-6 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .699
Extend: Algebra Lab Combinations and Pascal’s Triangle . . . . . . . . . . . . . . . . . . . . 704
10-7 Proof by Mathematical Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .705
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .710
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .715
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .716
Standardized Test Practice, Chapters 1–10 . . . . . . . . . . . . . . . . . . . . . . .718
F.IF.4
A.CED.4
A.SSE.4
A.APR.5
A.APR.5
A.SSE.1.b, A.APR.5
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Unit 1 | Foundations for Functions
Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Personal Tutor
pp. 724, 789Multilingual
eGlossary
pp. 722, 788
Vocabulary
pp. 742, 859Animation
pp. 720, 799
Unit 4 | Discrete Mathematics
Statistics Statistics and Probabilityand Probability
MIXA/Getty Im
ages
Statistics and Probability
Get Ready for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721
11-1 Designing a Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .723
Extend: Graphing Technology Lab Simulations and Margin of Error . . . . . . . . . . . . . 731
11-2 Distributions of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .733
11-3 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .742
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .751
11-4 The Binomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .752
11-5 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .760
Extend: Spreadsheet Lab Normal Approximation of Binomial Distributions . . . . . . . 767
11-6 Confidence Intervals and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . .769
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .777
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .781
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .782
Standardized Test Practice, Chapters 1–11 . . . . . . . . . . . . . . . . . . . . . . .784
S.IC.3, S.IC.5
S.IC.4, S.IC.6
S.IC.1
S.MD.7
S.MD.6, S.MD.7
S.ID.4
S.ID.4
S.IC.1, S.IC.4
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xiii xiii
Self-Check
Practice
pp. 738, 865
Foldables
pp. 722, 788Graphing
Calculator
pp. 731, 844
Virtual
Manipulatives
pp. 737, 822
Unit 5 | Trigonometry
Trigonometric Trigonometric FunctionsFunctions
Denn
is W
elsh
/Upp
erCu
t Im
ages
/Get
ty Im
ages
Trigonometric Functions
Get Ready for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787
Explore: Spreadsheet Lab Investigating Special Right Triangles . . . . . . . . . . . . . . . 789
12-1 Trigonometric Functions in Right Triangles. . . . . . . . . . . . . . . . . . . . . . . . .790
12-2 Angles and Angle Measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .799
Extend: Geometry Lab Areas of Parallelograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 806
12-3 Trigonometric Functions of General Angles . . . . . . . . . . . . . . . . . . . . . . . .807
12-4 Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .814
Extend: Geometry Lab Regular Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
12-5 Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .823
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .829
12-6 Circular and Periodic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .830
12-7 Graphing Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .837
Explore: Graphing Technology Lab Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . 844
12-8 Translations of Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .845
12-9 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .853
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .859
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .865
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .866
Standardized Test Practice, Chapters 1–12 . . . . . . . . . . . . . . . . . . . . . . .868
F.TF.1
F.TF.1, F.TF.2
F.IF.7.e, F.TF.5
F.BF.3
F.IF.7.e, F.BF.3
A.CED.2
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Unit 1 | Foundations for Functions
Your Digital Math PortalconnectED.mcgraw-hill.comccccc
Animation
p. 870
vvvvvvvvvv
Vocabulary
p. 873Multilingual
eGlossary
p. 872
Personal Tutor
p. 875
Unit 5 | Trigonometry
Trigonometric Identities Trigonometric Identities and Equationsand Equations
Self-Check
Practice
p. 897
Foldables
p. 872Graphing
Calculator
p. 900
Maria Teijeiro/Photodisc/Getty Im
ages
Trigonometric Identities and Equations
Get Ready for Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871
13-1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .873
13-2 Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .880
13-3 Sum and Difference of Angles Identities . . . . . . . . . . . . . . . . . . . . . . . . . . .886
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .892
13-4 Double-Angle and Half-Angle Identities . . . . . . . . . . . . . . . . . . . . . . . . . . .893
Explore: Graphing Technology Lab Solving Trigonometric Equations . . . . . . . . . . . . 900
13-5 Solving Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .901
Assessment
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .908
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .911
Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .912
Standardized Test Practice, Chapters 1–13 . . . . . . . . . . . . . . . . . . . . . . .914
F.TF.8
F.TF.8
F.TF.8
F.TF.8
F.TF.8
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Student HandbookStudent Handbook
Contents
How to Use the Student Handbook
Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1
Selected Answers and Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R14
Glossary/Glosario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R124
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R149
Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
Symbols and Parent Functions . . . . . . . . . . . . . . . . . . . . . . . . . Inside Back Cover
xv
Rubb
erba
ll/Ge
tty Im
ages
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