# Chapter 10: Quadratic Equations and Quadratic Functions

**At Grade**Created by: CK-12

## Introduction

Did you ever look at a rainbow and wonder about its shape? The arc a rainbow makes in the sky is a special type of curved function known as a parabola. A parabola is the graph of a quadratic function, which is the focus of this chapter. If you look closely, you’ll see parabolas in many aspects of everyday life. The hill on a roller coaster—that’s a parabola. The trajectory of water as it comes out of a drinking fountain—that’s a parabola. To model these real-life situations, you will use quadratic functions. This chapter will teach you how to graph functions and solve quadratic equations.

## Chapter Outline

- 10.1. Quadratic Functions and Their Graphs
- 10.2. Graphs of Quadratic Functions in Intercept Form
- 10.3. Use Graphs to Solve Quadratic Equations
- 10.4. Use Square Roots to Solve Quadratic Equations
- 10.5. Square Root Applications
- 10.6. Completing the Square
- 10.7. Vertex Form of a Quadratic Equation
- 10.8. Quadratic Formula
- 10.9. Comparing Methods for Solving Quadratics
- 10.10. Solutions Using the Discriminant
- 10.11. Linear, Exponential, and Quadratic Models
- 10.12. Applications of Function Models

### Chapter Summary

## Summary

The focus of this chapter is quadratic functions and equations. The chapter first deals with graphs of quadratic functions and then moves of to solving quadratic equations using such graphs. Quadratic functions in intercept form and vertex form are both covered. Other methods of solving quadratic equations, such as using square roots and completing the square, are the next topics of discussion. The chapter then moves on to using the Quadratic Formula to solve equations. A portion of this formula, called the discriminant, is dealt with in detail as a means of determining the nature of a quadratic equation’s solutions. The chapter closes with a discussion of linear, exponential, and quadratic models as well as introducing a method of comparing function models: regression.