SAMPLE College Algebra

Chapter 2: Inequalities and Quadratics

OVERVIEW The sections of this chapter are: 2.1 Inequalities 2.3 Sets and Intervals

2.2 Graphing Inequalities 2.4 Nonlinear Functions 2.5 Quadratics

Inequality is inherent in our perception - our eyes discern colors, shades, depths, and heights, while our ears detect variations in sound. These differences are communicated through inequalities, necessary for expressing variations in weight, temperature, and value. Quadratics, exemplified by the parabolic trajectory of a kicked or thrown ball, are familiar experiences for most people, mirrored in the arc of objects in motion. Water fountains, with their upward-spraying streams forming inverted parabolas, offer another common encounter with this mathematical concept. OBJECTIVES

By the end of the chapter, a student will be able to: • Describe inequalities, sets, and intervals in new ways • Recognize and describe nonlinear functions • Solve for an unknown variable • Multiply binomials • Apply the sign recognition method to solve quadratic equations • Apply the AC method to solve quadratic equations • Apply factoring formulas to factor and solve quadratic equations 2.1 Inequalities

Algebraic inequalities simply describe a difference like a difference in size, weight, length, temperature, or some value. We know that the temperature in a hot kitchen oven is higher than the temperature in a freezer. This can be communicated with an algebraic inequality. Temperature in a hot kitchen oven > temperature in a freezer Tip The > symbol means "greater than". It means that the quantity on the left is greater than the quantity on the right.