Algebra II Essentials for Dummies.

Intro -- Title Page -- Copyright Page -- Table of Contents -- Introduction -- About This Book -- Conventions Used in This Book -- Foolish Assumptions -- Icons Used in This Book -- Where to Go from Here -- Chapter 1 Making Advances in Algebra -- Bringing Out the Best in Algebraic Properties -- Making short work of the basic properties -- Organizing your operations -- Enumerating Exponential Rules -- Multiplying and dividing exponents -- Rooting out exponents -- Powering up exponents -- Working with negative exponents -- Assigning Factoring Techniques -- Making two terms factor -- Factoring three terms -- Factoring four or more terms by grouping -- Chapter 2 Lining Up Linear Equations -- Getting the First Degree: Linear Equations -- Solving basic linear equations -- Eliminating fractions -- Lining Up Linear Inequalities -- Solving basic inequalities -- Introducing interval notation -- Absolute Value: Keeping Everything in Line -- Solving absolute value equations -- Seeing through absolute value inequality -- Chapter 3 Making Quick Work of Quadratic Equations -- Using the Square Root Rule When Possible -- Solving Quadratic Equations by Factoring -- Factoring quadratic binomials -- Factoring quadratic trinomials -- The Quadratic Formula to the Rescue -- Realizing rational solutions -- Investigating irrational solutions -- Promoting Quadratic-like Equations -- Solving Quadratic Inequalities -- Keeping it strictly quadratic -- Signing up for fractions -- Increasing the number of factors -- Chapter 4 Rolling Along with Rational and Radical Equations -- Rounding Up Rational Equations and Eliminating Fractions -- Making your least common denominator work for you -- Proposing proportions for solving rational equations -- Reasoning with Radicals -- Squaring both sides of the equation -- Taking on two radicals -- Dealing with Negative Exponents.

Factoring out a negative exponent as a greatest common factor -- Solving quadratic-like trinomials -- Fiddling with Fractional Exponents -- Solving equations by factoring fractional exponents -- Promoting techniques for working with fractional exponents -- Chapter 5 Forging Function Facts -- Describing Function Characteristics -- Denoting function notation -- Using function notation to evaluate functions -- Determining Domain and Range -- Delving into domain -- Wrangling with range -- Counting on Even and Odd Functions -- Determining whether even or odd -- Using even and odd functions in graphs -- Taking on Functions One-to-One -- Defining which functions are one-to-one -- Testing for one-to-one functions -- Composing Functions -- Composing yourself with functions -- Composing with the difference quotient -- Getting into Inverse Functions -- Finding which functions are inverses -- Finding an inverse of a function -- Chapter 6 Graphing Linear and Quadratic Functions -- Identifying Some Graphing Techniques -- Finding x- and y-intercepts -- Reflecting on a graph's symmetry -- Mastering the Graphs of Lines -- Determining the slope of a line -- Describing two line equations -- Identifying parallel and perpendicular lines -- Coming to Terms with the Standard Form of a Quadratic -- Starting with "a" in the standard form -- Following "a" with "b" and "c" -- Eyeing a Quadratic's Intercepts -- Finding the one and only y-intercept -- Getting at the x-intercepts -- Finding the Vertex of a Parabola -- Computing vertex coordinates -- Linking up with the axis of symmetry -- Sketching a Graph from the Available Information -- Chapter 7 Pondering Polynomials -- Sizing Up a Polynomial Equation -- Identifying Intercepts and Turning Points -- Interpreting relative value and absolute value -- Dealing with intercepts and turning points.

Solving for y-intercepts and x-intercepts -- Determining When a Polynomial Is Positive or Negative -- Incorporating a sign line -- Recognizing a sign change rule -- Solving Polynomial Equations -- Factoring for roots -- Taking sane steps with the rational root theorem -- Putting Descartes in charge of signs -- Finding Roots Synthetically -- Using synthetic division when searching for roots -- Synthetically dividing by a binomial -- Chapter 8 Being Respectful of Rational Functions -- Examining Rational Functions -- Deliberating on domain -- Investigating intercepts -- Assigning Roles to Asymptotes -- Validating vertical asymptotes -- Finding equations for horizontal asymptotes -- Taking vertical and horizontal asymptotes to graphs -- Getting the scoop on oblique (slant) asymptotes -- Discounting Removable Discontinuities -- Finding removable discontinuities by factoring -- Evaluating the removals -- Looking at Limits of Rational Functions -- Determining limits at function discontinuities -- Finding infinity -- Looking at infinity -- Chapter 9 Examining Exponential and Logarithmic Functions -- Computing Exponentially -- Getting to the Base of Exponential Functions -- Classifying bases -- Introducing the more frequently used bases: 10 and e -- Exponential Equation Solutions -- Creating matching bases -- Quelling quadratic patterns -- Looking into Logarithmic Functions -- Presenting the properties of logarithms -- Doing more with logs than sawing -- Solving Equations Containing Logs -- Seeing all logs created equal -- Solving log equations by changing to exponentials -- Chapter 10 Getting Creative with Conics -- Posing with Parabolas -- Generalizing the form of a parabola's equation -- Making short work of a parabola's sketch -- Changing a parabola's equation to the standard form -- Circling around a Conic -- Getting Eclipsed by Ellipses.

Determining the shape -- Finding the foci -- Getting Hyped for Hyperbolas -- Including the asymptotes -- Graphing hyperbolas -- Chapter 11 Solving Systems of Equations -- Looking at Solutions Using the Standard Linear-Systems Form -- Solving Linear Systems by Graphing -- Interpreting an intersection -- Tackling the same line -- Putting up with parallel lines -- Using Elimination (Addition) to Solve Systems of Equations -- Finding Substitution to Be a Satisfactory Substitute -- Variable substituting made easy -- Writing solutions for coexisting lines -- Taking on Systems of Three Linear Equations -- Finding the solution of a system of three linear equations -- Generalizing with a system solution -- Increasing the Number of Equations -- Intersecting Parabolas and Lines -- Determining if and where lines and parabolas cross paths -- Determining that there's no solution -- Crossing Parabolas with Circles -- Finding multiple intersections -- Sifting through the possibilities for solutions -- Chapter 12 Taking the Complexity Out of Complex Numbers -- Simplifying Powers of i -- Getting More Complex with Complex Numbers -- Performing complex operations -- Performing complex division by multiplying by the conjugate -- Simplifying reluctant radicals -- Unraveling Complex Solutions in Quadratic Equations -- Investigating Polynomials with Complex Roots -- Classifying conjugate pairs -- Making use of complex zeros -- Chapter 13 Ten (or So) Special Formulas -- Using Multiplication to Add -- Factoring in Factorial -- Picking Out Permutations -- Collecting Combinations -- Adding n Integers -- Adding n Squared Integers -- Adding Odd Numbers -- Going for the Geometric -- Calculating Compound Interest -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.