Algebra II Workbook For Dummies

Mary Jane Sterling taught junior high and high school math before embarking on her career as an instructor at Bradley University, where she taught for more than 35 years.

• IntroductionAbout This Book 1Foolish Assumptions 2Icons Used in This Book 2Beyond the Book 3Where to Go from Here 3Part 1: Getting Started With Algebra II 5Chapter 1: Going Beyond Beginning Algebra 7Good Citizenship: Following the Order of Operations and Other Properties 7Specializing in Products and FOIL 10Variables on the Side: Solving Linear Equations 11Dealing with Linear Absolute Value Equations 12Greater Math Skills: Equalizing Linear Inequalities 14Answers to Problems on Going Beyond Beginning Algebra 16Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities 21Finding Reasonable Solutions with Radicals 22UnFOILed Again! Successfully Factoring for Solutions 23Your Bag of Tricks: Factoring Multiple Ways 25Keeping Your Act Together: Factoring by Grouping 26Resorting to the Quadratic Formula 27Solving Quadratics by Completing the Square 29Working with Quadratic-Like Equations 30Checking Out Quadratic Inequalities 32Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities 34Chapter 3: Rooting Out the Rational, the Radical, and the Negative 43Doing Away with Denominators with an LCD 44Simplifying and Solving Proportions 46Wrangling with Radicals 48Changing Negative Attitudes toward Negative Exponents 49Divided Powers: Solving Equations with Fractional Exponents 51Answers to Problems on Rooting Out the Rational, the Radical, and the Negative 53Chapter 4: Graphing for the Good Life 61Coordinating Axes, Coordinates of Points, and Quadrants 62Crossing the Line: Using Intercepts and Symmetry to Graph 64Graphing Lines Using Slope-Intercept and Standard Forms 67Graphing Basic Polynomial Curves 69Grappling with Radical and Absolute Value Functions 71Enter the Machines: Using a Graphing Calculator 73Answers to Problems on Graphing for the Good Life 77Part 2: Functions 89Chapter 5: Formulating Functions 91Evaluating Functions 91Determining the Domain and Range of a Function 93Recognizing Even, Odd, and One-to-One Functions 94Composing Functions and Simplifying the Difference Quotient 96Solving for Inverse Functions 99Answers to Problems on Formulating Functions 101Chapter 6: Specializing in Quadratic Functions 107Finding Intercepts and the Vertex of a Parabola 108Applying Quadratics to Real-Life Situations 109Graphing Parabolas 111Answers to Problems on Quadratic Functions 113Chapter 7: Plugging in Polynomials 119Finding Basic Polynomial Intercepts 120Digging up More-Difficult Polynomial Roots with Factoring 122Determining Where a Function Is Positive or Negative 123Graphing Polynomials 125Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes’s Rule 127Getting Real Results with Synthetic Division and the Remainder Theorem 130Connecting the Factor Theorem with a Polynomial’s Roots 132Answers to Problems on Plugging in Polynomials 134Chapter 8: Acting Rationally with Functions 143Determining Domain and Intercepts of Rational Functions 144Introducing Vertical and Horizontal Asymptotes 145Getting a New Slant with Oblique Asymptotes 147Removing Discontinuities 148Going the Limit: Limits at a Number and Infinity 149Graphing Rational Functions 151Answers to Problems on Rational Functions 156Chapter 9: Exposing Exponential and Logarithmic Functions 163Evaluating e-Expressions and Powers of e 164Solving Exponential Equations 165Making Cents: Applying Compound Interest and Continuous Compounding 167Checking out the Properties of Logarithms 169Presto-Chango: Expanding and Contracting Expressions with Log Functions 171Solving Logarithmic Equations 173They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions 175Answers to Problems on Exponential and Logarithmic Functions 179Part 3: Conics And Systems Of Equations 189Chapter 10: Any Way You Slice It: Conic Sections 191Putting Equations of Parabolas in Standard Form 192Shaping Up: Determining the Focus and Directrix of a Parabola 194Back to the Drawing Board: Sketching Parabolas 196Writing the Equations of Circles and Ellipses in Standard Form 198Determining Foci and Vertices of Ellipses 201Rounding Out Your Sketches: Circles and Ellipses 203Hyperbola: Standard Equations and Foci 205Determining the Asymptotes and Intercepts of Hyperbolas 206Sketching the Hyperbola 208Answers to Problems on Conic Sections 211Chapter 11: Solving Systems of Linear Equations 221Solving Two Linear Equations Algebraically 221Using Cramer’s Rule to Defeat Unruly Fractions 223A Third Variable: Upping the Systems to Three Linear Equations 225A Line by Any Other Name: Writing Generalized Solution Rules 227Decomposing Fractions Using Systems 229Answers to Problems on Systems of Equations 231Chapter 12: Solving Systems of Nonlinear Equations and Inequalities 237Finding the Intersections of Lines and Parabolas 237Crossing Curves: Finding the Intersections of Parabolas and Circles 239Appealing to a Higher Power: Dealing with Exponential Systems 240Solving Systems of Inequalities 242Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities 245Part 4: Other Good Stuff: Lists, Arrays, And Imaginary Numbers 251Chapter 13: Getting More Complex with Imaginary Numbers 253Simplifying Powers of i 254Not Quite Brain Surgery: Doing Operations on Complex Numbers 255“Dividing” Complex Numbers with a Conjugate 256Solving Equations with Complex Solutions 257Answers to Problems on Imaginary Numbers 259Chapter 14: Getting Squared Away with Matrices 263Describing Dimensions and Types of Matrices 263Adding, Subtracting, and Doing Scalar Multiplication on Matrices 265Trying Times: Multiplying Matrices by Each Other 267The Search for Identity: Finding Inverse Matrices 268Using Matrices to Solve Systems of Equations 272Answers to Problems on Matrices 274Chapter 15: Going Out of Sequence with Sequences and Series 279Writing the Terms of a Sequence 279Differences and Multipliers: Working with Special Sequences 282Backtracking: Constructing Recursively Defined Sequences 283Using Summation Notation 284Finding Sums with Special Series 286Answers to Problems on Sequences and Series 289Chapter 16: Everything You Ever Wanted to Know about Sets and Counting 293Writing the Elements of a Set from Rules or Patterns 294Get Together: Combining Sets with Unions, Intersections, and Complements 295Multiplication Countdowns: Simplifying Factorial Expressions 297Checking Your Options: Using the Multiplication Property 298Counting on Permutations When Order Matters 300Mixing It Up with Combinations 301Raising Binomials to Powers: Investigating the Binomial Theorem 303Answers to Problems on Sets and Counting 304Part 5: The Part Of Tens 309Chapter 17: Basic Graphs 311Putting Polynomials in Their Place 311Lining Up Front and Center 312Being Absolutely Sure with Absolute Value 313Graphing Reciprocals of x and x2 .313Rooting Out Square Root and Cube Root .314Growing Exponentially with a Graph 315Logging In on Logarithmic Graphing 316Chapter 18: Ten Special Sequences and Their Sums 317Adding as Easy as One, Two, Three 317Summing Up the Squares 318Finding the Sum of the Cubes 318Not Being at Odds with Summing Odd Numbers 319Evening Things Out by Adding Up Even Numbers 319Adding Everything Arithmetic 319Geometrically Speaking 320Easing into a Sum for e 320Signing In on the Sine 321Powering Up on Powers of 2 322Adding Up Fractions with Multiples for Denominators 322Index 323