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Boost your chances of scoring higher at Algebra II

Algebra II introduces students to complex algebra concepts in preparation for trigonometry and calculus. In this new edition of Algebra II Workbook For Dummies, high school and college students will work through the types of Algebra II problems they´ll see in class, including systems of equations, matrices, graphs, and conic sections. Plus, the book now comes with free 1-year access to chapter quizzes online!

A recent report by ACT shows that over a quarter of ACT-tested 2012 high school graduates did not meet any of the four college readiness benchmarks in mathematics, English, reading, and science. Algebra II Workbook For Dummies presents tricky topics in plain English and short lessons, with examples and practice at every step to help students master the essentials, setting them up for success with each new lesson.

Tracks to a typical Algebra II class
Can be used as a supplement to classroom learning or for test prep
Includes plenty of practice and examples throughout
Comes with free access to chapter quizzes online
Get ready to take the intimidation out of Algebra II!



TABLE OF CONTENTS
Introduction

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 2

Beyond the Book 3

Where to Go from Here 3

Part 1: Getting Started with Algebra II 5

Chapter 1: Going Beyond Beginning Algebra 7

Good Citizenship: Following the Order of Operations and Other Properties 7

Specializing in Products and FOIL 10

Variables on the Side: Solving Linear Equations 11

Dealing with Linear Absolute Value Equations 12

Greater Math Skills: Equalizing Linear Inequalities 14

Answers to Problems on Going Beyond Beginning Algebra 16

Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities 21

Finding Reasonable Solutions with Radicals 22

UnFOILed Again! Successfully Factoring for Solutions 23

Your Bag of Tricks: Factoring Multiple Ways 25

Keeping Your Act Together: Factoring by Grouping 26

Resorting to the Quadratic Formula 27

Solving Quadratics by Completing the Square 29

Working with Quadratic-Like Equations 30

Checking Out Quadratic Inequalities 32

Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities 34

Chapter 3: Rooting Out the Rational, the Radical, and the Negative 43

Doing Away with Denominators with an LCD 44

Simplifying and Solving Proportions 46

Wrangling with Radicals 48

Changing Negative Attitudes toward Negative Exponents 49

Divided Powers: Solving Equations with Fractional Exponents 51

Answers to Problems on Rooting Out the Rational, the Radical, and the Negative 53

Chapter 4: Graphing for the Good Life 61

Coordinating Axes, Coordinates of Points, and Quadrants 62

Crossing the Line: Using Intercepts and Symmetry to Graph 64

Graphing Lines Using Slope-Intercept and Standard Forms 67

Graphing Basic Polynomial Curves 69

Grappling with Radical and Absolute Value Functions 71

Enter the Machines: Using a Graphing Calculator 73

Answers to Problems on Graphing for the Good Life 77

Part 2: Functions 89

Chapter 5: Formulating Functions 91

Evaluating Functions 91

Determining the Domain and Range of a Function 93

Recognizing Even, Odd, and One-to-One Functions 94

Composing Functions and Simplifying the Difference Quotient 96

Solving for Inverse Functions 99

Answers to Problems on Formulating Functions 101

Chapter 6: Specializing in Quadratic Functions 107

Finding Intercepts and the Vertex of a Parabola 108

Applying Quadratics to Real-Life Situations 109

Graphing Parabolas 111

Answers to Problems on Quadratic Functions 113

Chapter 7: Plugging in Polynomials 119

Finding Basic Polynomial Intercepts 120

Digging up More-Difficult Polynomial Roots with Factoring 122

Determining Where a Function Is Positive or Negative 123

Graphing Polynomials 125

Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes's Rule 127

Getting Real Results with Synthetic Division and the Remainder Theorem 130

Connecting the Factor Theorem with a Polynomial's Roots 132

Answers to Problems on Plugging in Polynomials 134

Chapter 8: Acting Rationally with Functions 143

Determining Domain and Intercepts of Rational Functions 144

Introducing Vertical and Horizontal Asymptotes 145

Getting a New Slant with Oblique Asymptotes 147

Removing Discontinuities 148

Going the Limit: Limits at a Number and Infinity 149

Graphing Rational Functions 151

Answers to Problems on Rational Functions 156

Chapter 9: Exposing Exponential and Logarithmic Functions 163

Evaluating e-Expressions and Powers of e 164

Solving Exponential Equations 165

Making Cents: Applying Compound Interest and Continuous Compounding 167

Checking out the Properties of Logarithms 169

Presto-Chango: Expanding and Contracting Expressions with Log Functions 171

Solving Logarithmic Equations 173

They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions 175

Answers to Problems on Exponential and Logarithmic Functions 179

Part 3: Conics and Systems of Equations 189

Chapter 10: Any Way You Slice It: Conic Sections 191

Putting Equations of Parabolas in Standard Form 192

Shaping Up: Determining the Focus and Directrix of a Parabola 194

Back to the Drawing Board: Sketching Parabolas 196

Writing the Equations of Circles and Ellipses in Standard Form 198

Determining Foci and Vertices of Ellipses 201

Rounding Out Your Sketches: Circles and Ellipses 203

Hyperbola: Standard Equations and Foci 205

Determining the Asymptotes and Intercepts of Hyperbolas 206

Sketching the Hyperbola 208

Answers to Problems on Conic Sections 211

Part 3: Conics and Systems of Equations 189

Solving Two Linear Equations Algebraically 221

Using Cramer's Rule to Defeat Unruly Fractions 223

A Third Variable: Upping the Systems to Three Linear Equations 225

A Line by Any Other Name: Writing Generalized Solution Rules 227

Decomposing Fractions Using Systems 229

Answers to Problems on Systems of Equations 231

Part 3: Conics and Systems of Equations 189

Finding the Intersections of Lines and Parabolas 237

Crossing Curves: Finding the Intersections of Parabolas and Circles 239

Appealing to a Higher Power: Dealing with Exponential Systems 240

Solving Systems of Inequalities 242

Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities 245

Part 4: Other Good Stuff: Lists, Arrays, and Imaginary Numbers 251

Chapter 13: Getting More Complex with Imaginary Numbers 253

Simplifying Powers of i 254

Not Quite Brain Surgery: Doing Operations on Complex Numbers 255

"Dividingö Complex Numbers with a Conjugate 256

Solving Equations with Complex Solutions 257

Answers to Problems on Imaginary Numbers 259

Chapter 14: Getting Squa