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Preparing for Advanced Algebra Get Started On Chapter 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P2 Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P3 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 Table of Contents 0-1 Ed Freeman/Stone/Getty Images Posttest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P29 c connectED.mcgraw-hill.com Vocabulary p. P4 Your Digital Math Portal Multilingual eGlossary Personal Tutor Foldables p. P6 p. P2 p. P2 i Unit 1 | Linear Relations and Functions Equations and Inequalities Mathematical Content Get Ready for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1-1 Expressions and Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 A.SSE.1.a, A.SSE.1.b 1-2 Properties of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 A.SSE.2 1-3 Solving Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 A.CED.1 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 1-4 Solving Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 A.SSE.1.b, A.CED.1 1-5 Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 A.CED.1, A.CED.3 Explore: Algebra Lab Interval Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1-6 Solving Compound and Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . .41 A.CED.1, A.CED.3 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 Standardized Test Practice, Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 Jon Boyes/Photographer’s Choice/Getty Images c connectED.mcgraw-hill.com Your Digital Math Portal Animation Vocabulary pp. 12, 84 pp. 5, 69 Multilingual eGlossary pp. 4, 60 ii Personal Tutor pp. 6, 63 Unit 1 | Linear Relations and Functions Linear Relations and Functions Mathematical Content 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 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 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 2-5 Scatter Plots and Lines of Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 F.IF.4 Extend: Algebra Lab Correlation and Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 F.IF.4 2-6 Special Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Explore: Graphing Technology Lab Families of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . 108 Roine Magnusson/Photodisc/Getty Images 2-7 Parent Functions and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2-8 Graphing Linear and Absolute Value Inequalities. . . . . . . . . . . . . . . . . . . . . . 117 F.IF.4, F.IF.7.b F.BF.3 F.IF.4, F.BF.3 A.CED.3 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Standardized Test Practice, Chapters 1–2 . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Virtual Manipulatives Graphing Calculator pp. 28, 61 p. 90 Foldables pp. 4, 60 Self-Check Practice pp. 7, 127 iii Unit 1 | Linear Relations and Functions Systems of Equations and Inequalities Mathematical Content Get Ready for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Explore: Graphing Technology Lab Intersections of Graphs . . . . . . . . . . . . . . . . . . . . . 135 3-1 Solving Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.CED.3, A.REI.11 3-2 Solving Systems of Inequalities by Graphing . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.CED.3 Extend: Graphing Technology Lab Systems of Linear Inequalities . . . . . . . . . . . . . . . . 153 3-3 Optimization with Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 A.CED.3 3-4 Systems of Equations in Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 A.CED.3 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 A.CED.3 3-8 Solving Systems of Equations Using Inverse Matrices. . . . . . . . . . . . . . . . . . 198 A.CED.3 DreamPictures/Blend Images/Getty Images 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 c connectED.mcgraw-hill.com Your Digital Math Portal Animation Vocabulary pp. 146, 247 pp. 206, 290 Multilingual eGlossary pp. 134, 218 iv Personal Tutor pp. 136, 222 Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations Quadratic Functions Functions Quadratic and Relations Relations and Mathematical Content 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 A.SSE.1.a, F.IF.9 F.IF.4 A.CED.2, F.IF.4 A.REI.11 4-3 Solving Quadratic Equations by Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 A.SSE.2, F.IF.8.a 4-4 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 N.CN.1, N.CN.2 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 Black 100/Allsport Concepts/Getty Images 4-8 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 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 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 Virtual Manipulatives Graphing Calculator pp. 137, 219 pp. 205, 237 Foldables pp. 134, 218 Self-Check Practice pp. 183, 295 v Unit 2 1 | FoundationsPolynomial, Quadratic, for Functions and Radical Functions and Relations 5 Polynomialsand and Polynomials P PolynomialFunctions Functions Polynomial P Mathematical Content Get Ready for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 5-1 Operations with Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 A.APR.1 Extend: Algebra Lab Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 5-2 Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 A.APR.6 Extend: Graphing Technology Lab Dividing Polynomials . . . . . . . . . . . . . . . . . . . . . . . 318 A.APR.6 Explore: Graphing Technology Lab Power Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 320 F.IF.4 5-3 Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 F.IF.4, F.IF.7.c 5-4 Analyzing Graphs of Polynomial Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 330 F.IF.4, F.IF.7.c Extend: Graphing Technology Lab Modeling Data Using Polynomial Functions . . . . . . 338 F.IF.4, F.IF.7.c Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Explore: Graphing Technology Lab Solving Polynomial Equations by Graphing . . . . . . 341 5-5 Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 A.CED.1 Extend: Graphing Technology Lab Polynomial Identities . . . . . . . . . . . . . . . . . . . . . . . 350 A.REI.11 5-6 The Remainder and Factor Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 A.APR.2, F.IF.7.c 5-7 Roots and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 N.CN.9, A.APR.3 Extend: Graphing Technology Lab Analyzing Polynomial Functions . . . . . . . . . . . . . . . 366 A.APR.4 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 c connectED.mcgraw-hill.com Your Digital Math Portal Vocabulary pp. 306, 387 pp. 303, 400 Multilingual eGlossary pp. 302, 384 vi Personal Tutor pp. 304, 386 Photodisc/Getty Images Animation Unit 2 | Quadratic, Polynomial, and Radical Functions and Relations 6 I Inverses and Radical F Functions and Relations Mathematical Content Get Ready for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 6-1 Operations on Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 F.IF.9, F.BF.1.b 6-2 Inverse Functions and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 F.IF.4, F.BF.4.a Extend: Graphing Technology Lab Inverse Functions and Relations. . . . . . . . . . . . . . . 399 6-3 Square Root Functions and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 F.IF.7.b, F.BF.3 6-4 nth Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 A.SSE.2 Extend: Graphing Technology Lab Graphing nth Root Functions . . . . . . . . . . . . . . . . . 413 F.IF.7.b, F.BF.3 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 6-5 Operations with Radical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 A.SSE.2 6-6 Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 6-7 Solving Radical Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 429 Extend: Graphing Technology Lab Solving Radical Equations and Inequalities. . . . . . . 436 A.REI.2 A.REI.2, A.REI.11 Stockbyte/Getty Images Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Standardized Test Practice, Chapters 1–6 . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Virtual Manipulatives Graphing Calculator p. 331 pp. 338, 436 Foldables pp. 302, 384 Self-Check Practice pp. 326, 443 vii Unit 3 1 | Foundations Advanced Functions for Functions and Relations Exponential and Logarithmic Functions and Relations Mathematical Content Get Ready for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 7-1 Graphing Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Explore: Graphing Technology Lab Solving Exponential Equations and Inequalities . . . 459 F.IF.7.e, F.IF.8.b A.REI.11 7-2 Solving Exponential Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . 461 A.CED.1, F.LE.4 7-3 Logarithms and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 F.IF.7.e, F.BF.3 Extend: Graphing Technology Lab Choosing the Best Model . . . . . . . . . . . . . . . . . . . . 476 7-4 Solving Logarithmic Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . 478 A.SSE.2, A.CED.1 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 7-5 Properties of Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 A.CED.1 7-6 Common Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 A.CED.1 Extend: Graphing Technology Lab Solving Logarithmic Equations and Inequalities . . . 499 A.REI.11 7-7 Base e and Natural Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 A.SSE.2 Explore: Spreadsheet Lab Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 7-8 Using Exponential and Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . 509 Extend: Graphing Technology Lab Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 F.IF.8.b, F.LE.4 F.BF.1.b Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 Standardized Test Practice, Chapters 1–7 . . . . . . . . . . . . . . . . . . . . . . . . . . 524 c connectED.mcgraw-hill.com Your Digital Math Portal Vocabulary pp. 453, 532 pp. 517, 581 Multilingual eGlossary pp. 450, 528 viii Personal Tutor pp. 455, 531 Purestock/Getty Images Animation Unit 3 | Advanced Functions and Relations Rational Functions and Relations Mathematical Content Get Ready for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 8-1 Multiplying and Dividing Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . 529 A.APR.7 8-2 Adding and Subtracting Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . . 538 A.APR.7 8-3 Graphing Reciprocal Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 A.CED.2, F.BF.3 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 8-4 Graphing Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 A.CED.2, F.IF.9 Extend: Graphing Technology Lab Graphing Rational Functions . . . . . . . . . . . . . . . . . 561 8-5 Variation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 A.CED.2 8-6 Solving Rational Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . 570 A.CED.1, A.REI.2 Extend: Graphing Technology Lab Solving Rational Equations and Inequalities . . . . . . 579 A.REI.2, A.REI.11 Image Source/Masterfile Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Standardized Test Practice, Chapters 1–8 . . . . . . . . . . . . . . . . . . . . . . . . . . 588 Virtual Manipulatives Graphing Calculator pp. 451, 557 pp. 516, 579 Foldables pp. 450, 528 Self-Check Practice pp. 464, 585 ix Unit 3 1 | Foundations Advanced Functions for Functions and Relations Conic Sections Mathematical Content Get Ready for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 9-1 Midpoint and Distance Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 A.CED.4 9-2 Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 A.SSE.1.b, A.CED.2 Explore: Graphing Technology Lab Equations of Circles . . . . . . . . . . . . . . . . . . . . . 606 9-3 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 A.SSE.1.b, A.CED.4 Explore: Algebra Lab Investigating Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 9-4 Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 A.SSE.1.b, A.CED.2 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 9-5 Hyperbolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 A.SSE.1.b, A.CED.2 9-6 Identifying Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 A.SSE.1.b, F.IF.9 Extend: Graphing Technology Lab Analyzing Quadratic Relations . . . . . . . . . . . . . . 637 Explore: Graphing Technology Lab Linear-Nonlinear Systems . . . . . . . . . . . . . . . . . 639 9-7 Solving Linear-Nonlinear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 A.REI.11 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 Standardized Test Practice, Chapters 1–9 . . . . . . . . . . . . . . . . . . . . . . . . 654 Your Digital Math Portal Animation Vocabulary pp. 641, 659 pp. 599, 710 Multilingual eGlossary pp. 592, 658 x Personal Tutor pp. 600, 660 Brand X Pictures/PunchStock c connectED.mcgraw-hill.com Unit 4 | Discrete Mathematics Sequences and Sequences and Series Series Mathematical Content Get Ready for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 10-1 Sequences as Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 F.IF.4 10-2 Arithmetic Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666 A.CED.4 10-3 Geometric Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 A.SSE.4 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 Martin Child/Photodisc/Getty Images 10-7 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 A.APR.5 Extend: Algebra Lab Combinations and Pascal’s Triangle . . . . . . . . . . . . . . . . . . . . 704 A.APR.5 Proof by Mathematical Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 A.SSE.1.b, A.APR.5 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 710 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 Standardized Test Practice, Chapters 1–10 . . . . . . . . . . . . . . . . . . . . . . . 718 Virtual Manipulatives Graphing Calculator pp. 594, 681 pp. 639, 690 Foldables pp. 592, 658 Self-Check Practice pp. 603, 715 xi Unit 4 1 | Foundations Discrete Mathematics for Functions Statistics and Probability Mathematical Content Get Ready for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721 11-1 Designing a Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 S.IC.3, S.IC.5 Extend: Graphing Technology Lab Simulations and Margin of Error. . . . . . . . . . . . . 731 S.IC.4, S.IC.6 11-2 Distributions of Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733 S.IC.1 11-3 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742 S.MD.7 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 11-4 The Binomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 S.MD.6, S.MD.7 11-5 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 S.ID.4 Extend: Spreadsheet Lab Normal Approximation of Binomial Distributions . . . . . . . 767 S.ID.4 11-6 Confidence Intervals and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . 769 S.IC.1, S.IC.4 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782 Standardized Test Practice, Chapters 1–11 . . . . . . . . . . . . . . . . . . . . . . . 784 c connectED.mcgraw-hill.com Your Digital Math Portal Vocabulary pp. 720, 799 pp. 742, 859 Multilingual eGlossary pp. 722, 788 xii Personal Tutor pp. 724, 789 MIXA/Getty Images Animation Unit 5 | Trigonometry Trigonometric Functions Mathematical Content 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 F.TF.1 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 F.TF.1, F.TF.2 12-7 Graphing Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837 F.IF.7.e, F.TF.5 Dennis Welsh/UpperCut Images/Getty Images Explore: Graphing Technology Lab Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . 844 F.BF.3 12-8 Translations of Trigonometric Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845 F.IF.7.e, F.BF.3 12-9 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853 A.CED.2 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 Standardized Test Practice, Chapters 1–12 . . . . . . . . . . . . . . . . . . . . . . . 868 Virtual Manipulatives Graphing Calculator pp. 737, 822 pp. 731, 844 Foldables pp. 722, 788 Self-Check Practice pp. 738, 865 xiii Unit 5 1 | Foundations for Functions Trigonometry Trigonometric Identities and Equations Mathematical Content Get Ready for Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871 13-1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873 F.TF.8 13-2 Verifying Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880 F.TF.8 13-3 Sum and Difference of Angles Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . 886 F.TF.8 Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892 13-4 Double-Angle and Half-Angle Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . 893 F.TF.8 Explore: Graphing Technology Lab Solving Trigonometric Equations . . . . . . . . . . . . 900 13-5 Solving Trigonometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 F.TF.8 Assessment Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 911 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 912 Standardized Test Practice, Chapters 1–13 . . . . . . . . . . . . . . . . . . . . . . . 914 Maria Teijeiro/Photodisc/Getty Images c connectED.mcgraw-hill.com Animation Vocabulary p. 870 p. 873 Your Digital Math Portal Multilingual eGlossary p. 872 xiv v Personal Tutor p. 875 Graphing Calculator p. 900 Foldables p. 872 Self-Check Practice p. 897 Student Handbook Contents How to Use the Student Handbook Rubberball/Getty Images 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