Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra II For Dummies and Algebra II Workbook For Dummies.

Select Guide Rating

• Introduction 1About This Book 1Conventions Used in This Book 2Foolish Assumptions 2Icons Used in This Book 2Where to Go from Here 3Chapter 1: Making Advances in Algebra 5Bringing Out the Best in Algebraic Properties 5Making short work of the basic properties 6Organizing your operations 7Enumerating Exponential Rules 8Multiplying and dividing exponents 8Rooting out exponents 9Powering up exponents 10Working with negative exponents 10Assigning Factoring Techniques 10Making two terms factor 11Factoring three terms 12Factoring four or more terms by grouping 13Chapter 2: Lining Up Linear Equations 15Getting the First Degree: Linear Equations 15Solving basic linear equations 16Eliminating fractions 16Lining Up Linear Inequalities 17Solving basic inequalities 18Introducing interval notation 19Absolute Value: Keeping Everything in Line 20Solving absolute value equations 20Seeing through absolute value inequality 21Chapter 3: Making Quick Work of Quadratic Equations 23Using the Square Root Rule When Possible 24Solving Quadratic Equations by Factoring 24Factoring quadratic binomials 25Factoring quadratic trinomials 26The Quadratic Formula to the Rescue 27Realizing rational solutions 27Investigating irrational solutions 27Promoting Quadratic-like Equations 28Solving Quadratic Inequalities 29Keeping it strictly quadratic 30Signing up for fractions 31Increasing the number of factors 33Chapter 4: Rolling Along with Rational and Radical Equations 35Rounding Up Rational Equations and Eliminating Fractions 35Making your least common denominator work for you 36Proposing proportions for solving rational equations 38Reasoning with Radicals 39Squaring both sides of the equation 39Taking on two radicals 40Dealing with Negative Exponents 42Factoring out a negative exponent as a greatest common factor 42Solving quadratic-like trinomials 43Fiddling with Fractional Exponents 44Solving equations by factoring fractional exponents 44Promoting techniques for working with fractional exponents 44Chapter 5: Forging Function Facts 47Describing Function Characteristics 47Denoting function notation 48Using function notation to evaluate functions 48Determining Domain and Range 49Delving into domain 49Wrangling with range 50Counting on Even and Odd Functions 51Determining whether even or odd 52Using even and odd functions in graphs 53Taking on Functions One-to-One 53Defining which functions are one-to-one 54Testing for one-to-one functions 54Composing Functions 55Composing yourself with functions 55Composing with the difference quotient 56Getting into Inverse Functions 57Finding which functions are inverses 58Finding an inverse of a function 59Chapter 6: Graphing Linear and Quadratic Functions 61Identifying Some Graphing Techniques 61Finding x- and y-intercepts 62Reflecting on a graph’s symmetry 62Mastering the Graphs of Lines 64Determining the slope of a line 64Describing two line equations 65Identifying parallel and perpendicular lines 67Coming to Terms with the Standard Form of a Quadratic 67Starting with “a” in the standard form 68Following “a” with “b” and “c” 69Eyeing a Quadratic’s Intercepts 69Finding the one and only y-intercept 69Getting at the x-intercepts 70Finding the Vertex of a Parabola 71Computing vertex coordinates 71Linking up with the axis of symmetry 72Sketching a Graph from the Available Information 72Chapter 7: Pondering Polynomials 75Sizing Up a Polynomial Equation 75Identifying Intercepts and Turning Points 76Interpreting relative value and absolute value 76Dealing with intercepts and turning points 77Solving for y-intercepts and x-intercepts 78Determining When a Polynomial is Positive or Negative 79Incorporating a sign line 79Recognizing a sign change rule 80Solving Polynomial Equations 81Factoring for roots 81Taking sane steps with the rational root theorem 82Putting Descartes in charge of signs 84Finding Roots Synthetically 86Using synthetic division when searching for roots 86Synthetically dividing by a binomial 88Chapter 8: Being Respectful of Rational Functions 91Examining Rational Functions 91Deliberating on domain 92Investigating intercepts 92Assigning Roles to Asymptotes 93Validating vertical asymptotes 93Finding equations for horizontal asymptotes 94Taking vertical and horizontal asymptotes to graphs 94Getting the scoop on oblique (slant) asymptotes 96Discounting Removable Discontinuities 97Finding removable discontinuities by factoring 97Evaluating the removals 98Looking at Limits of Rational Functions 99Determining limits at function discontinuities 100Finding infinity 102Looking at infinity 104Chapter 9: Examining Exponential and Logarithmic Functions 107Computing Exponentially 107Getting to the Base of Exponential Functions 108Classifying bases 108Introducing the more frequently used bases: 10 and e 110Exponential Equation Solutions 110Creating matching bases 111Quelling quadratic patterns 111Looking into Logarithmic Functions 113Presenting the properties of logarithms 113Doing more with logs than sawing 115Solving Equations Containing Logs 117Seeing all logs created equal 117Solving log equations by changing to exponentials 118Chapter 10: Getting Creative with Conics 121Posing with Parabolas 122Generalizing the form of a parabola’s equation 123Making short work of a parabola’s sketch 124Changing a parabola’s equation to the standard form 125Circling around a Conic 126Getting Eclipsed by Ellipses 127Determining the shape 129Finding the foci 130Getting Hyped for Hyperbolas 130Including the asymptotes 131Graphing hyperbolas 132Chapter 11: Solving Systems of Equations 135Looking at Solutions Using the Standard Linear-Systems Form 136Solving Linear Systems by Graphing 136Interpreting an intersection 137Tackling the same line 137Putting up with parallel lines 137Using Elimination (Addition) to Solve Systems of Equations 138Finding Substitution to Be a Satisfactory Substitute 139Variable substituting made easy 139Writing solutions for coexisting lines 140Taking on Systems of Three Linear Equations 141Finding the solution of a system of three linear equations 141Generalizing with a system solution 143Increasing the Number of Equations 144Intersecting Parabolas and Lines 146Determining if and where lines and parabolas cross paths 147Determining that there’s no solution 149Crossing Parabolas with Circles 150Finding multiple intersections 150Sifting through the possibilities for solutions 151Chapter 12: Taking the Complexity Out of Complex Numbers 155Simplifying Powers of i 156Getting More Complex with Complex Numbers 157Performing complex operations 157Performing complex division by multiplying by the conjugate 158Simplifying reluctant radicals 159Unraveling Complex Solutions in Quadratic Equations 160Investigating Polynomials with Complex Roots 160Classifying conjugate pairs 161Making use of complex zeros 161Chapter 13: Ten (or So) Special Formulas 163Using Multiplication to Add 163Factoring in Factorial 164Picking Out Permutations 164Collecting Combinations 164Adding n Integers 165Adding n Squared Integers 165Adding Odd Numbers 165Going for the Geometric 166Calculating Compound Interest 166Index 167