Algebra and Trigonometry, 5th Edition

3.2 Quadratic Equations, Functions, Zeros, and Models

• Find zeros of quadratic functions and solve quadratic equations by using the principle of zero products, by using the principle of square roots, by completing the square, and by using the quadratic formula.

• Solve equations that are reducible to quadratic.

• Solve applied problems using quadratic equations.

Quadratic Equations and Quadratic Functions

In this section, we will explore the relationship between the solutions of quadratic equations and the zeros of quadratic functions. We define quadratic equations and quadratic functions as follows.

Quadratic Equations

A quadratic equation is an equation that can be written in the form

$$a{x}^2+bx+c=0,a\ne 0,$$

where a, b, and c are real numbers.