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UNIT 1 EQUATIONS AND INEQUALITIES Planning the Unit 1a Unit 1 Overview 1 Getting Ready 2

Activity 1 Investigating Patterns—Cross-Country Adventures 3 Lesson 1-1 Numeric and Graphic Representations of Data 3 Lesson 1-2 Writing Expressions 8 Activity 1 Practice 14

Activity 2 Solving Equations—What’s My Number? 15 Lesson 2-1 Writing and Solving Equations 15 Lesson 2-2 Equations with Variables on Both Sides 19 Lesson 2-3 Solving More Complex Equations 22 Lesson 2-4 Equations with No Solution or Infinitely Many Solutions 25 Lesson 2-5 Solving Literal Equations for a Variable 28 Activity 2 Practice 31

Embedded Assessment 1 Patterns and Equations—Of Music and Money 33

Activity 3 Solving Inequalities—Physical Fitness Zones 35 Lesson 3-1 Inequalities and Their Solutions 35 Lesson 3-2 Solving Inequalities 38 Lesson 3-3 Compound Inequalities 43 Activity 3 Practice 47

Activity 4 Absolute Value Equations and Inequalities—Student Distances 49 Lesson 4-1 Absolute Value Equations 49 Lesson 4-2 Absolute Value Inequalities 54 Activity 4 Practice 59

Embedded Assessment 2 Inequalities and Absolute Value—Diet and Exercise 61

UNIT 2 FUNCTIONS Planning the Unit 63a Unit 2 Overview 63 Getting Ready 64

Activity 5 Functions and Function Notation—Vending Machines 65 Lesson 5-1 Relations and Functions 65 Lesson 5-2 Domain and Range 71 Lesson 5-3 Function Notation 76 Activity 5 Practice 79

Activity 6 Interpreting Graphs of Functions—Shake, Rattle, and Roll 81 Lesson 6-1 Key Features of Graphs 81 Lesson 6-2 More Complex Graphs 87 Lesson 6-3 Graphs of Real-World Situations 92 Activity 6 Practice 95

To the Teacher xi

Instructional Units

Contents v

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Activity 7 Graphs of Functions—Experiment Experiences 97 Lesson 7-1 The Spring Experiment 97 Lesson 7-2 The Falling Object Experiment 101 Lesson 7-3 The Radioactive Decay Experiment 105 Activity 7 Practice 109

Activity 8 Transformations of Functions—Transformers 111 Lesson 8-1 Exploring f(x) + k 111 Lesson 8-2 Exploring f(x + k) 115 Activity 8 Practice 119

Embedded Assessment 1 Representations of Functions—Bryce Canyon Hiking 121

Activity 9 Rates of Change—Ramp It Up 123 Lesson 9-1 Slope 123 Lesson 9-2 Slope and Rate of Change 128 Lesson 9-3 More About Slopes 133 Activity 9 Practice 137

Activity 10 Linear Models—Stacking Boxes 139 Lesson 10-1 Direct Variation 139 Lesson 10-2 Indirect Variation 144 Lesson 10-3 Another Linear Model 148 Lesson 10-4 Inverse Functions 152 Activity 10 Practice 157

Activity 11 Arithmetic Sequences—Picky Patterns 159 Lesson 11-1 Identifying Arithmetic Sequences 159 Lesson 11-2 A Formula for Arithmetic Sequences 162 Lesson 11-3 Arithmetic Sequences as Functions 166 Activity 11 Practice 171

Embedded Assessment 2 Linear Functions and Equations—Text Message Plans 173

Activity 12 Forms of Linear Functions—Under Pressure 175 Lesson 12-1 Slope-Intercept Form 175 Lesson 12-2 Point-Slope Form 179 Lesson 12-3 Standard Form 183 Lesson 12-4 Slopes of Parallel and Perpendicular Lines 187 Activity 12 Practice 191

Activity 13 Equations from Data—Pass the Book 193 Lesson 13-1 Scatter Plots and Trend Lines 193 Lesson 13-2 Linear Regression 197 Lesson 13-3 Quadratic and Exponential Regressions 200 Activity 13 Practice 205

Embedded Assessment 3 Linear Models and Slope as Rate of Change— A 10K Run 207

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UNIT 3 EXTENSIONS OF LINEAR CONCEPTS Planning the Unit 209a Unit 3 Overview 209 Getting Ready 210

Activity 14 Piecewise-Defined Linear Functions—Breakfast for Bowser 211 Lesson 14-1 Function Notation and Rate of Change 211 Lesson 14-2 Writing Functions and Finding Domain and Range 215 Lesson 14-3 Evaluating Functions and

Graphing Piecewise-Defined Linear Functions 219 Lesson 14-4 Comparing Functions 221 Activity 14 Practice 225

Activity 15 Comparing Equations—A Tale of a Trucker 227 Lesson 15-1 Writing Equations from Graphs and Tables 227 Lesson 15-2 Comparing Functions with Inequalities 231 Lesson 15-3 Writing Equations from Verbal Descriptions 235 Activity 15 Practice 237

Activity 16 Inequalities in Two Variables—Shared Storage 239 Lesson 16-1 Writing and Graphing Inequalities in Two Variables 239 Lesson 16-2 Graphing Inequalities in Two Variables 242 Activity 16 Practice 247

Embedded Assessment 1 Graphing Inequalities and Piecewise-Defined Functions—Earnings on a Graph 249

Activity 17 Solving Systems of Linear Equations—A Tale of Two Truckers 251 Lesson 17-1 The Graphing Method 251 Lesson 17-2 Using Tables and the Substitution Method 256 Lesson 17-3 The Elimination Method 261 Lesson 17-4 Systems Without a Unique Solution 264 Lesson 17-5 Classifying Systems of Equations 267 Activity 17 Practice 271

Activity 18 Solving Systems of Linear Inequalities—Which Region Is It? 273 Lesson 18-1 Representing the Solution of a System of Inequalities 273 Lesson 18-2 Interpreting the Solution of a System of Inequalities 278 Activity 18 Practice 281

Embedded Assessment 2 Systems of Equations and Inequalities—Tilt the Scales 283

UNIT 4 EXPONENTS, RADICALS, AND POLYNOMIALS Planning the Unit 285a Unit 4 Overview 285 Getting Ready 286

Activity 19 Exponent Rules—Icebergs and Exponents 287 Lesson 19-1 Basic Exponent Properties 287 Lesson 19-2 Negative and Zero Powers 291 Lesson 19-3 Additional Properties of Exponents 294 Activity 19 Practice 297

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Activity 20 Operations with Radicals—Go Fly a Kite 299 Lesson 20-1 Radical Expressions 299 Lesson 20-2 Adding and Subtracting Radical Expressions 304 Lesson 20-3 Multiplying and Dividing Radical Expressions 307 Activity 20 Practice 311

Activity 21 Geometric Sequences—Go Viral! 313 Lesson 21-1 Identifying Geometric Sequences 313 Lesson 21-2 Formulas for Geometric Sequences 316 Activity 21 Practice 321

Embedded Assessment 1 Exponents, Radicals, and Geometric Sequences— Taking Stock 323

Activity 22 Exponential Functions—Protecting Your Investment 325 Lesson 22-1 Exponential Functions and Exponential Growth 325 Lesson 22-2 Exponential Decay 329 Lesson 22-3 Graphs of Exponential Functions 333 Activity 22 Practice 339

Activity 23 Modeling with Exponential Functions—Growing, Growing, Gone 341 Lesson 23-1 Compound Interest 341 Lesson 23-2 Population Growth 347 Activity 23 Practice 351

Embedded Assessment 2 Exponential Functions—Family Bonds 353

Activity 24 Adding and Subtracting Polynomials—Polynomials in the Sun 355 Lesson 24-1 Polynomial Terminology 355 Lesson 24-2 Adding Polynomials 359 Lesson 24-3 Subtracting Polynomials 364 Activity 24 Practice 367

Activity 25 Multiplying Polynomials—Tri-Com Computers 369 Lesson 25-1 Multiplying Binomials 369 Lesson 25-2 Special Products of Binomials 376 Lesson 25-3 Multiplying Polynomials 379 Activity 25 Practice 381

Embedded Assessment 3 Polynomial Operations—Measuring Up 383

Activity 26 Factoring—Factors of Construction 385 Lesson 26-1 Factoring by Greatest Common Factor (GCF) 385 Lesson 26-2 Factoring Special Products 388 Activity 26 Practice 391

Activity 27 Factoring Trinomials—Deconstructing Floor Plans 393 Lesson 27-1 Factoring x2 + bx + c 393 Lesson 27-2 Factoring ax2 + bx + c 398 Activity 27 Practice 401

Activity 28 Simplifying Rational Expressions—Totally Rational 403 Lesson 28-1 Simplifying Rational Expressions 403

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Lesson 28-2 Dividing Polynomials 406 Lesson 28-3 Multiplying and Dividing Rational Expressions 411 Lesson 28-4 Adding and Subtracting Rational Expressions 413 Activity 28 Practice 417

Embedded Assessment 4 Factoring and Simplifying Rational Expressions— Rock Star Demands 419

UNIT 5 QUADRATIC FUNCTIONS Planning the Unit 421a Unit 5 Overview 421 Getting Ready 422

Activity 29 Introduction to Quadratic Functions—Touchlines 423 Lesson 29-1 Modeling with a Quadratic Function 423 Lesson 29-2 Graphing and Analyzing a Quadratic Function 427 Activity 29 Practice 431

Activity 30 Graphing Quadratic Functions—Transformers 433 Lesson 30-1 Translations of the Quadratic Parent Function 433 Lesson 30-2 Stretching and Shrinking the Quadratic Parent Function 440 Lesson 30-3 Multiple Transformations of the Quadratic Parent Function 444 Activity 30 Practice 451

Embedded Assessment 1 Graphing Quadratic Functions—Parabolic Paths 453

Activity 31 Solving Quadratic Equations by Graphing and Factoring— Trebuchet Trials 455 Lesson 31-1 Solving by Graphing or Factoring 455 Lesson 31-2 The Axis of Symmetry and the Vertex 459 Lesson 31-3 Graphing a Quadratic Function 462 Activity 31 Practice 465

Activity 32 Algebraic Methods of Solving Quadratic Equations— Keeping It Quadratic 467 Lesson 32-1 The Square Root Method 467 Lesson 32-2 Completing the Square 471 Lesson 32-3 The Quadratic Formula 474 Lesson 32-4 Choosing a Method and Using the Discriminant 477 Lesson 32-5 Complex Solutions 480 Activity 32 Practice 483

Activity 33 Applying Quadratic Equations—Rockets in Flight 485 Lesson 33-1 Fitting Data with a Quadratic Function 485 Lesson 33-2 Interpreting Solutions of Quadratic Equations 488 Activity 33 Practice 491

Embedded Assessment 2 Solving Quadratic Equations—Egg Drop 493

Activity 34 Graphs of Functions—Photo App 495 Lesson 34-1 Constructing Models 495 Lesson 34-2 Comparing Models 500

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Lesson 34-3 Extending Models 503 Activity 34 Practice 507

Activity 35 Systems of Equations—Population Explosion 509 Lesson 35-1 Solving a System Graphically 509 Lesson 35-2 Solving a System Algebraically 513 Activity 35 Practice 517

Embedded Assessment 3 Solving Systems of Equations—Sports Collector 519

UNIT 6 PROBABILITY AND STATISTICS Planning the Unit 521a Unit 6 Overview 521 Getting Ready 522

Activity 36 Measures of Center and Spread—To Text, or Not to Text 523 Lesson 36-1 Mean, Median, Mode, and MAD 523 Lesson 36-2 Another Measure of Variability 532 Activity 36 Practice 536

Activity 37 Dot and Box Plots and the Normal Distribution— Disturbing Coyotes 537 Lesson 37-1 Dot Plots and Box Plots 537 Lesson 37-2 Modified Box Plots 543 Lesson 37-3 Normally Distributed 548 Activity 37 Practice 554

Embedded Assessment 1 Comparing Univariate Distributions—Splitting the Bill 557

Activity 38 Correlation—What’s the Relationship? 559 Lesson 38-1 Scatter Plots 559 Lesson 38-2 Correlation Coefficient 564 Activity 38 Practice 569

Activity 39 The Best-Fit Line—Regressing Linearly 571 Lesson 39-1 Line of Best Fit 571 Lesson 39-2 Residuals 577 Lesson 39-3 Interpreting the Slope and Intercept of the Best-Fit Line 582 Lesson 39-4 Plotting Residuals 588 Activity 39 Practice 594

Activity 40 Bivariate Data—Categorically Speaking 595 Lesson 40-1 Bivariate Categorical Data 595 Lesson 40-2 Presenting Relative Frequency Data Graphically 600 Activity 40 Practice 607

Embedded Assessment 2 Bivariate Distributions—Dear Traveling Tooth 609

RESOURCES 613 Formulas 614 Learning Strategies 618 Glossary 621 Academic Vocabulary Graphic Organizers 626

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