Algebra II Workbook For Dummies

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 Chapter 11: Solving Systems of Linear Equations 221 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 Chapter 12: Solving Systems of Nonlinear Equations and Inequalities 237 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 “Dividing” Complex Numbers with a Conjugate 256 Solving Equations with Complex Solutions 257 Answers to Problems on Imaginary Numbers 259 Chapter 14: Getting Squared Away with Matrices 263 Describing Dimensions and Types of Matrices 263 Adding, Subtracting, and Doing Scalar Multiplication on Matrices 265 Trying Times: Multiplying Matrices by Each Other 267 The Search for Identity: Finding Inverse Matrices 268 Using Matrices to Solve Systems of Equations 272 Answers to Problems on Matrices 274 Chapter 15: Going Out of Sequence with Sequences and Series 279 Writing the Terms of a Sequence 279 Differences and Multipliers: Working with Special Sequences 282 Backtracking: Constructing Recursively Defined Sequences 283 Using Summation Notation 284 Finding Sums with Special Series 286 Answers to Problems on Sequences and Series 289 Chapter 16: Everything You Ever Wanted to Know about Sets and Counting 293 Writing the Elements of a Set from Rules or Patterns 294 Get Together: Combining Sets with Unions, Intersections, and Complements 295 Multiplication Countdowns: Simplifying Factorial Expressions 297 Checking Your Options: Using the Multiplication Property 298 Counting on Permutations When Order Matters 300 Mixing It Up with Combinations 301 Raising Binomials to Powers: Investigating the Binomial Theorem 303 Answers to Problems on Sets and Counting 304 Part 5: The Part Of Tens 309 Chapter 17: Basic Graphs 311 Putting Polynomials in Their Place 311 Lining Up Front and Center 312 Being Absolutely Sure with Absolute Value 313 Graphing Reciprocals of x and x2 .313 Rooting Out Square Root and Cube Root .314 Growing Exponentially with a Graph 315 Logging In on Logarithmic Graphing 316 Chapter 18: Ten Special Sequences and Their Sums 317 Adding as Easy as One, Two, Three 317 Summing Up the Squares 318 Finding the Sum of the Cubes 318 Not Being at Odds with Summing Odd Numbers 319 Evening Things Out by Adding Up Even Numbers 319 Adding Everything Arithmetic 319 Geometrically Speaking 320 Easing into a Sum for e 320 Signing In on the Sine 321 Powering Up on Powers of 2 322 Adding Up Fractions with Multiples for Denominators 322 Index 323