QUADRATIC EQUATIONS, INEQUALITIES, AND FUNCTIONS College Algebra

Factoring and Completing the Square Review of factoring Review of the even-root property Completing the square Radicals and rational expressions Imaginary solutions

The Q uadratic Formula Developing the formula Using the formula Number of solutions Applications

Additional Topics Writing a quadratic equation with given solutions Using the discriminant in factoring Equations quadratic in form Applications

Quadratic Functions and Their Graphs Quadratic functions Graphing quadratic functions The vertex and intercepts Applications

Quadratic and Rational Inequalities Solving quadratic inequalities with a sign graph Perfect square inequalities Solving rational inequalities with a sign graph Quadratic inequalities that cannot be factored Applications

Graphs and Functions of Relations Linear and constant functions Absolute value functions Quadratic functions Square-root functions Piecewise functions Graphing relations

Transformations of Graphs Reflecting Translating Stretching and shrinking Multiple transformations

Combining Functions Basic operations with functions Composition

Inverse Functions Inverse of a function Identifying inverse functions Switch-and-solve strategy Even roots or even powers Graphs of f and f -1

Variation in Functions Direct, inverse, and joint variation Finding the variation constant Finding a new value for the dependent variable Applications