
Algebra II Essentials For Dummies
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Content
- 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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