Table Of Content

Series Author and Senior Consultant Marian Small Lead Author Chris Kirkpatrick Authors Andrew Dmytriw • Beverly Farahani • Angelo Lillo Kay Minter • David Pilmer • Noel Walker Functions and Applications 11 Series Author and Senior Authors Senior Consultant Consultant Andrew Dmytriw, Beverly David Zimmer Marian Small Farahani, Angelo Lillo, Kay Minter, David Pilmer, Noel Walker Math Consultant Lead Author Kaye Appleby Chris Kirkpatrick Contributing Authors Kathleen Kacuiba, Ralph Montesanto, Krista Zupan General Manager, Mathematics, Contributing Editors Interior Design Science, and Technology Amanda Allan, Alasdair Graham, Peter Papayanakis Lenore Brooks First Folio Resource Group, Inc., Tom Shields, Robert Templeton, Cover Design Publisher, Mathematics First Folio Resource Group, Inc., Eugene Lo Colin Garnham Caroline Winter Cover Image Associate Publisher, Mathematics Editorial Assistant Pierre Berton Resource Library, Sandra McTavish Caroline Winter Vaughan, Tom Arban Photography Inc. 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Reviewers and Advisory Panel Paul Alves Punitha Kandasamy Grace Mlodzianowski Mathematics Department Head Classroom Teacher (Secondary— Mathematics Department Head Stephen Lewis Secondary School Mathematics) Cardinal Newman High School Peel District School Board Mississauga Secondary School Toronto Catholic District School Board Mississauga, ON Peel District School Board Toronto, ON Mississauga, ON Terri Blackwell Elizabeth Pattison Mathematics Teacher Halyna Kopach Head of Mathematics Burlington Central High School Mathematics Department Head Westlane Secondary School Halton District School Board Mary Ward Catholic Secondary School District School Board of Niagara Burlington, ON Toronto Catholic District School Board Niagara Falls, ON Toronto, ON Heather Boychuk Joshua Plant Program Leader of Mathematics Richard Long Mathematics Teacher Lasalle Secondary School Mathematics Department Head Huntsville High School Rainbow District School Board Centennial Secondary School Trillium Lakelands District School Board Sudbury, ON Hastings and Prince Edward District Huntsville, ON School Board Karen Bryan Belleville, ON Patricia Steele Program Resource Teacher, Numeracy Mathematics Resource Teacher & Literacy 7–12 Susan MacRury Simcoe County District School Board Upper Canada District School Board Mathematics Teacher Midhurst, ON Brockville, ON Lasalle Secondary School Rainbow District School Board Scott Taylor Justin De Weerdt Sudbury, ON Head of Mathematics, Business, and Mathematics Department Head Computer Science Huntsville High School Frank Maggio Bell High School Trillium Lakelands District School Board Department Head of Mathematics Ottawa-Carleton District School Board Huntsville, ON Holy Trinity High School Nepean, ON Halton Catholic District School Board Robert Donato Oakville, ON Dave Wright Secondary Mathematics Resource Mathematics Teacher Teacher Peter Matijosaitis Woburn Collegiate Institute Toronto Catholic District School Board Mathematics Department Head Toronto District School Board Toronto, ON Loretto Abbey Catholic Secondary Toronto, ON School Richard Gallant Toronto Catholic District School Board Charles Wyszkowski Secondary Curriculum Consultant Toronto, ON Instructor Simcoe Muskoka Catholic District School of Education School Board Cheryl McQueen Trent University Barrie, ON Mathematics Learning Coordinator, Peterborough, ON 7–12 Jacqueline Hill Thames Valley District School Board Krista Zupan K–12 Mathematics Facilitator London, ON Resource Teacher for Student Success Durham District School Board Durham Catholic District School Board Whitby, ON Ian McTavish Oshawa, ON Librarian/Mathematics Teacher Huntsville High School Trillium Lakelands District School Board Huntsville, ON iii Table of Contents Chapter 1: Introduction to the Curious Math 117 Quadratic Function 1 Chapter Review 118 Getting Started 2 Chapter Self-Test 122 1.1 The Characteristics of a Function 6 Chapter Task 123 1.2 Comparing Rates of Change in Linear and Quadratic Functions 17 Chapter 3: Working with Quadratic Curious Math 26 Functions: Standard and Factored Forms 124 1.3 Working with Function Notation 27 Getting Started 126 Mid-Chapter Review 36 3.1 Exploring a Situation Using a Quadratic 1.4 Exploring Transformations of Quadratic Functions 38 Function 130 3.2 Relating the Standard and Factored Forms 132 1.5 Graphing Quadratic Functions by Using Transformations 41 3.3 Solving Quadratic Equations by Graphing 143 1.6 Using Multiple Transformations to Graph Mid-Chapter Review 153 Quadratic Functions 51 3.4 Solving Quadratic Equations by Factoring 156 1.7 The Domain and Range of a Quadratic Function 59 3.5 Solving Problems Involving Quadratic Functions 164 Chapter Review 66 3.6 Creating a Quadratic Model from Data 170 Chapter Self-Test 70 Curious Math 180 Chapter Task 71 Chapter Review 181 Chapter Self-Test 184 Chapter 2: The Algebra of Quadratic Chapter Task 185 Expressions 72 Getting Started 74 Chapters 1–3 Cumulative Review 186 2.1 Working with Quadratic Expressions 78 2.2 Factoring Polynomials: Common Factoring 88 Chapter 4: Working with Quadratic 2.3 Factoring Quadratic Expressions: Models: Standard and Vertex Forms 190 x2(cid:1)bx(cid:1)c 95 Getting Started 192 Mid-Chapter Review 101 4.1 The Vertex Form of a Quadratic Function 196 2.4 Factoring Quadratic Expressions: 4.2 Relating the Standard and Vertex Forms: ax2 (cid:1) bx(cid:1)c 104 Completing the Square 206 2.5 Factoring Quadratic Expressions: Special 4.3 Solving Quadratic Equations Using the Cases 111 Quadratic Formula 216 Table of Contents v Curious Math 224 6.3 Investigating the Sine Function 335 Mid-Chapter Review 225 6.4 Comparing Sinusoidal Functions 344 4.4 Investigating the Nature of the Roots 227 Curious Math 354 4.5 Using Quadratic Function Models to Solve Mid-Chapter Review 355 Problems 234 6.5 Transformations of the Sine Function: 4.6 Using the Vertex Form to Create Quadratic f(x) (cid:2)sin(x(cid:3)c) and f(x) (cid:2)sin x(cid:1)d 359 Function Models from Data 242 6.6 More Transformations of sin x: Chapter Review 253 f(x) (cid:2)asin x 368 Chapter Self-Test 256 Chapter Review 377 Chapter Task 257 Chapter Self-Test 380 Chapter Task 381 Chapter 5: Trigonometry and Acute Triangles 258 Chapters 4–6 Cumulative Review 382 Getting Started 260 5.1 Applying the Primary Trigonometric Ratios 264 Chapter 7: Exponential Functions 386 5.2 Solving Problems by Using Right- Getting Started 388 Triangle Models 274 7.1 Collecting Exponential Data 392 5.3 Investigating and Applying the Sine Law in Acute Triangles 283 7.2 The Laws of Exponents 395 7.3 Working with Integer Exponents 402 Mid-Chapter Review 291 7.4 Working with Rational Exponents 410 5.4 Investigating and Applying the Cosine Law in Acute Triangles 294 Mid-Chapter Review 418 5.5 Solving Problems by Using Acute- 7.5 Exploring the Properties of Exponential Triangle Models 302 Functions 420 7.6 Solving Problems Involving Exponential Curious Math 312 Growth 425 Chapter Review 313 7.7 Problems Involving Exponential Decay 433 Chapter Self-Test 316 Curious Math 441 Chapter Task 317 Chapter Review 442 Chapter Self-Test 446 Chapter 6: Sinusoidal Functions 318 Chapter Task 447 Getting Started 320 6.1 Exploring Periodic Motion 324 6.2 Periodic Behaviour 326 vi Table of Contents Chapter 8: Solving Financial Problems Curious Math 520 Involving Exponential Functions 448 Chapter Review 521 Getting Started 450 Chapter Self-Test 524 8.1 Investigating Interest and Rates of Change 454 Chapter Task 525 8.2 Compound Interest: Determining Future Value 462 Chapters 7–8 Cumulative Review 526 8.3 Compound Interest: Determining Present Value 471 Appendix A: Review of Essential 8.4 Compound Interest: Solving Financial Skills and Knowledge 528 Problems 479 Appendix B: Review of Technical Skills 558 Mid-Chapter Review 489 Glossary 584 8.5 Regular Annuities: Determining Future Value 493 Answers 591 8.6 Regular Annuities: Determining Index 653 Present Value 501 Credits 656 8.7 Savings Plans and Loans: Creating Amortization Tables 509 Table of Contents vii Chapter 1 Introduction to the Quadratic Function GOALS You will be able to • Use appropriate notation to describe relationships as functions • Graph linear and quadratic functions • Model linear and quadratic relationships • Use transformations to relate different quadratic functions ? 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