# Chapter 9: Two Solutions Are Better Than One?

**Advanced**Created by: CK-12

**Introduction**

In this chapter you will extend your knowledge about quadratic equations and functions. You will learn to solve a quadratic equation by graphing, by using the quadratic formula and by completing the square. These methods will then be applied to solving real world problems dealing with quadratic equations. The solutions of quadratic equations will go beyond the real numbers to include imaginary roots. The discriminant will also be used to determine the nature of the roots of a quadratic equation. The sum and the product of the roots will be used to determine a quadratic equation.

This chapter will also conclude with solving quadratic inequalities and solving radical equations.

**Lessons**

In this chapter you will do the following lessons:

- Solving quadratic equations by graphing
- The zeros of the quadratic function
- Solving a quadratic equation using the quadratic formula
- Solving quadratic equations by completing the square
- Real-world applications of quadratic equations
- Imaginary roots of a quadratic equation
- Using the discriminant to determine the nature of the roots of the quadratic equation
- Solving radical equations
- Determining the solution of a quadratic inequality

## Chapter Outline

- 9.1. Solving Quadratic Equations by Graphing
- 9.2. Solving Quadratic Equations by Completing the Square
- 9.3. Solving Quadratic Equations Using the Quadratic Formula
- 9.4. Applications of Quadratic Equations
- 9.5. Using the Roots to Determine the Quadratic Equation
- 9.6. Complex and Imaginary Numbers
- 9.7. The Discriminant
- 9.8. Radical Equations
- 9.9. Chapter Test