EQUATIONS, INEQUALITIES, FUNCTIONS Planning the Unit Unit 1 Overview 1 Getting Ready 2

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1 v-x_sb_a2_te_fm_toc.indd Page 5 15/04/14 1:55 PM user-g-w-728 To the Teacher Instructional Units UNIT 1 EQUATIONS, INEQUALITIES, FUNCTIONS 1a Unit 1 Overview 1 Getting Ready 2 Activity 1 Creating Equations One to Two 3 Lesson 1-1 One-Variable Equations 3 Lesson 1-2 Two-Variable Equations 7 Lesson 1-3 Absolute Value Equations and Inequalities 11 Activity 1 Practice 15 Activity 2 Graphing to Find Solutions Choices 17 Lesson 2-1 Graphing Two-Variable Equations 17 Lesson 2-2 Graphing Systems of Inequalities 21 Activity 2 Practice 27 Activity 3 Systems of Linear Equations Monetary Systems Overload 29 Lesson 3-1 Solving Systems of Two Equations in Two Variables 29 Lesson 3-2 Solving Systems of Three Equations in Three Variables 36 Lesson 3-3 Matrix Operations 42 Lesson 3-4 Solving Matrix Equations 47 Activity 3 Practice 53 Embedded Assessment 1 Equations, Inequalities, and Systems Gaming Systems 55 Activity 4 Piecewise-Defined Functions Absolutely Piece-ful 57 Lesson 4-1 Introduction to Piecewise-Defined Functions 57 Lesson 4-2 Step Functions and Absolute Value Functions 61 Lesson 4-3 Transforming the Absolute Value Parent Function 65 Activity 4 Practice 71 Activity 5 Function Composition and Operations New from Old 73 Lesson 5-1 Operations with Functions 73 Lesson 5-2 Function Composition 79 Lesson 5-3 More Function Composition 84 Activity 5 Practice 87 Activity 6 Inverse Functions Old from New 89 Lesson 6-1 Finding Inverse Functions 89 Lesson 6-2 Graphs of Inverse Functions 93 Activity 6 Practice 97 Embedded Assessment 2 Piecewise-Defined, Composite, and Inverse Functions Currency Conversion 99 UNIT 2 QUADRATIC FUNCTIONS 101a Unit 2 Overview 101 Getting Ready 102 xi v

2 v-x_sb_a2_te_fm_toc.indd Page 6 15/04/14 1:55 PM user-g-w-728 continued Activity 7 Applications of Quadratic Functions Fences 103 Lesson 7-1 Analyzing a Quadratic Function 103 Lesson 7-2 Factoring Quadratic Expressions 107 Lesson 7-3 Solving Quadratic Equations by Factoring 111 Lesson 7-4 More Uses for Factors 116 Activity 7 Practice 119 Activity 8 Introduction to Complex Numbers Cardano s Imaginary Numbers 121 Lesson 8-1 The Imaginary Unit, i 121 Lesson 8-2 Operations with Complex Numbers 126 Lesson 8-3 Factoring with Complex Numbers 132 Activity 8 Practice 135 Activity 9 Solving ax 2 + bx + c = 0 Deriving the Quadratic Formula 137 Lesson 9-1 Completing the Square and Taking Square Roots 137 Lesson 9-2 The Quadratic Formula 141 Lesson 9-3 Solutions of Quadratic Equations 144 Activity 9 Practice 149 Embedded Assessment 1 Applications of Quadratic Functions and Equations No Horsing Around 151 Activity 10 Writing Quadratic Equations What Goes Up Must Come Down 153 Lesson 10-1 Parabolas and Quadratic Equations 153 Lesson 10-2 Writing a Quadratic Function Given Three Points 163 Lesson 10-3 Quadratic Regression 167 Activity 10 Practice 171 Activity 11 Transformations of y = x 2 Parent Parabola 173 Lesson 11-1 Translations of Parabolas 173 Lesson 11-2 Shrinking, Stretching, and Reflecting Parabolas 178 Lesson 11-3 Vertex Form 186 Activity 11 Practice 189 Embedded Assessment 2 Writing and Transforming Quadratic Functions The Safari Experience 191 Activity 12 Graphing Quadratics and Quadratic Inequalities Calendar Art 193 Lesson 12-1 Key Features of Quadratic Functions 193 Lesson 12-2 More Key Features of Quadratic Functions 197 Lesson 12-3 Graphing Quadratic Functions 200 Lesson 12-4 The Discriminant 204 Lesson 12-5 Graphing Quadratic Inequalities 206 Activity 12 Practice 209 Activity 13 Systems of Linear and Nonlinear Equations Supply and Demand 211 Lesson 13-1 Solving a System Graphically 211 Lesson 13-2 Solving a System Algebraically 217 Activity 13 Practice 221 Embedded Assessment 3 Graphing Quadratic Functions and Solving Systems The Green Monster 223 vi SpringBoard Mathematics Algebra 2

3 v-x_sb_a2_te_fm_toc.indd Page 7 15/04/14 1:55 PM user-g-w-728 UNIT 3 POLYNOMIALS 225a Unit 3 Overview 225 Getting Ready 226 Activity 14 Introduction to Polynomials Postal Service 227 Lesson 14-1 Polynomials 227 Lesson 14-2 Some Attributes of Polynomial Functions 231 Lesson 14-3 Even and Odd Functions 237 Activity 14 Practice 239 Activity 15 Polynomial Operations Polly s Pasta 241 Lesson 15-1 Adding and Subtracting Polynomials 241 Lesson 15-2 Multiplying Polynomials 245 Lesson 15-3 Dividing Polynomials 248 Activity 15 Practice 253 Activity 16 Binomial Theorem Pascal s Triangle 255 Lesson 16-1 Introduction to Pascal s Triangle 255 Lesson 16-2 Applying the Binomial Theorem 259 Activity 16 Practice 263 Embedded Assessment 1 Polynomial Operations This Test is Square 265 Activity 17 Factors of Polynomials How Many Roots? 267 Lesson 17-1 Algebraic Methods 267 Lesson 17-2 The Fundamental Theorem of Algebra 271 Activity 17 Practice 275 Activity 18 Graphs of Polynomials Getting to the End Behavior 277 Lesson 18-1 Graphing Polynomial Functions 277 Lesson 18-2 Finding the Roots of a Polynomial Function 281 Lesson 18-3 Comparing Polynomial Functions 287 Activity 18 Practice 289 Embedded Assessment 2 Factoring and Graphing Polynomials Sketch Artist 291 UNIT 4 SERIES, EXPONENTIAL AND LOGARITHMIC FUNCTIONS 293a Unit 4 Overview 293 Getting Ready 294 Activity 19 Arithmetic Sequences and Series Arithmetic Alkanes 295 Lesson 19-1 Arithmetic Sequences 295 Lesson 19-2 Arithmetic Series 299 Lesson 19-3 Sigma Notation 303 Activity 19 Practice 305 Activity 20 Geometric Sequences and Series Squares with Patterns 307 Lesson 20-1 Geometric Sequences 307 Lesson 20-2 Geometric Series 312 Lesson 20-3 Convergence of Series 317 Activity 20 Practice 319 vii

4 v-x_sb_a2_te_fm_toc.indd Page 8 15/04/14 1:55 PM user-g-w-728 continued Embedded Assessment 1 Sequences and Series The Chessboard Problem 321 Activity 21 Exponential Functions and Graphs Sizing Up the Situation 323 Lesson 21-1 Exploring Exponential Patterns 323 Lesson 21-2 Exponential Functions 326 Lesson 21-3 Exponential Graphs and Asymptotes 329 Lesson 21-4 Transforming Exponential Functions 331 Lesson 21-5 Natural Base Exponential Functions 336 Activity 21 Practice 341 Activity 22 Logarithms and Their Properties Earthquakes and Richter Scale 343 Lesson 22-1 Exponential Data 343 Lesson 22-2 The Common Logarithm Function 348 Lesson 22-3 Properties of Logarithms 350 Lesson 22-4 More Properties of Logarithms 353 Activity 22 Practice 355 Embedded Assessment 2 Exponential Functions and Common Logarithms Whether or Not 357 Activity 23 Inverse Functions: Exponential and Logarithmic Functions Undoing It All 359 Lesson 23-1 Logarithms in Other Bases 359 Lesson 23-2 Properties of Logarithms and the Change of Base Formula 362 Lesson 23-3 Graphs of Logarithmic Functions 365 Activity 23 Practice 369 Activity 24 Logarithmic and Exponential Equations and Inequalities College Costs 371 Lesson 24-1 Exponential Equations 371 Lesson 24-2 Solving Equations by Using Logarithms 373 Lesson 24-3 Logarithmic Equations 376 Lesson 24-4 Exponential and Logarithmic Inequalities 379 Activity 24 Practice 381 Embedded Assessment 3 Exponential and Logarithmic Equations Evaluating Your Interest 383 UNIT 5 RADICAL AND RATIONAL FUNCTIONS 385a Unit 5 Overview 385 Getting Ready 386 Activity 25 Square Root and Cube Root Functions Go, Boat, Go! 387 Lesson 25-1 Square Root Functions 387 Lesson 25-2 Solving Square Root Equations 391 Lesson 25-3 Cube Root Functions 394 Lesson 25-4 Solving Cube Root Equations 397 Activity 25 Practice 399 viii SpringBoard Mathematics Algebra 2

5 v-x_sb_a2_te_fm_toc.indd Page 9 15/04/14 1:55 PM user-g-w-728 Activity 26 Inverses: Roots, Squares, and Cubes Swing, Swing, Swing 401 Lesson 26-1 Square Root Functions and Regressions 401 Lesson 26-2 Square Root and Quadratic Functions 406 Lesson 26-3 Cube Root and Cubic Functions 410 Activity 26 Practice 413 Embedded Assessment 1 Radical Functions: Square Roots, Cube Roots, and Their Inverses How Big is That Ball? 415 Activity 27 Introduction to Rational Functions Planning a Summer Camp 417 Lesson 27-1 Formulating and Graphing a Rational Function 417 Lesson 27-2 Formulating and Graphing More Rational Functions 421 Lesson 27-3 Identifying Asymptotes 425 Activity 27 Practice 429 Activity 28 Inverse Variation and Rational Functions Stream Survival 431 Lesson 28-1 Inverse Variation and Combined Variation 431 Lesson 28-2 Transformations of the Parent Rational Function 435 Activity 28 Practice 441 Embedded Assessment 2 Rational Functions and Variation A Condo for My Cat 443 Activity 29 Simplifying Rational Expressions It s All Rational 445 Lesson 29-1 Multiplying and Dividing Rational Expressions 445 Lesson 29-2 Adding and Subtracting Rational Expressions 449 Lesson 29-3 Finding Horizontal and Vertical Asymptotes 453 Lesson 29-4 Graphing Rational Functions 457 Activity 29 Practice 461 Activity 30 Rational Equations and Inequalities A Rational Pastime 463 Lesson 30-1 Solving Rational Equations 463 Lesson 30-2 Solving Rational Inequalities 467 Activity 30 Practice 471 Embedded Assessment 3 Rational Expressions, Equations, and Inequalities Work It Out! 473 UNIT 6 TRIGONOMETRY 475a Unit 6 Overview 475 Getting Ready 476 Activity 31 Understanding Radian Measure Revolving Restaurant 477 Lesson 31-1 Radian Measure 477 Lesson 31-2 Applying Radian Measure 482 Activity 31 Practice 485 Activity 32 Trigonometric Functions Which Angle is Up? 487 Lesson 32-1 Placing the Unit Circle on the Coordinate Plane 487 Lesson 32-2 Special Right Triangles and the Unit Circle 494 Activity 32 Practice 499 ix

6 v-x_sb_a2_te_fm_toc.indd Page 10 15/04/14 1:55 PM user-g-w-728 continued Activity 33 Trigonometric Identities: Pythagorean Connection More Than Just Triangles 501 Lesson 33-1 The Pythagorean Identity 501 Lesson 33-2 Other Trigonometric Identities 504 Activity 33 Practice 507 Embedded Assessment 1 Radians, Unit Circles, and Trigonometry A Floral Clock 509 Activity 34 Graphs of Trigonometric Functions Creation of a Mural 511 Lesson 34-1 Periodic Functions 511 Lesson 34-2 The Sine Function 515 Lesson 34-3 The Cosine Function 521 Lesson 34-4 The Tangent Function 527 Lesson 34-5 Translating Trigonometric Functions 533 Activity 34 Practice 539 Activity 35 Choosing Functions to Model Periodic Phenomena The Sky Wheel 541 Lesson 35-1 Modeling Periodic Phenomena 541 Activity 35 Practice 547 Embedded Assessment 2 Trigonometric Functions Totally Tires 549 UNIT 7 PROBABILITY AND STATISTICS 551a Unit 7 Overview 551 Getting Ready 552 Activity 36 Normal Distribution Take Me Out to the Ballgame 553 Lesson 36-1 Shapes of Distributions 553 Lesson 36-2 Characteristics of the Normal Distribution 558 Lesson 36-3 z-scores and their Probabilities 562 Lesson 36-4 Modeling with the Normal Distribution 568 Activity 36 Practice 573 Activity 37 Random Sampling Part-Time Jobs 577 Lesson 37-1 Surveys 577 Lesson 37-2 Experiments 582 Lesson 37-3 Observational Studies 586 Activity 37 Practice 589 Embedded Assessment 1 Normal Models, Surveys, and Experiments Researching Readers 591 Activity 38 Simulations Is Martin Improving? 593 Lesson 38-1 Devising Simulations 593 Lesson 38-2 Confirming Data with Simulations 600 Activity 38 Practice 604 Activity 39 Margin of Error Can't Get No Satisfaction 605 Lesson 39-1 Introduction to Margin of Error 605 Lesson 39-2 Computing Margin of Error 611 Activity 39 Practice 618 x SpringBoard Mathematics Algebra 2