# 11: Quadratic Equations and Applications

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## Learning Objectives

By the end of this chapter, the student should be able to

• Solve quadratics by the square root property, completing the square, and using the quadratic formula
• Graph a quadratic function by using properties or transformations
• Solve quadratic inequalities by graphing, or algebraically
• Find the extreme value of a quadratic function
• Solve applications and functions using quadratic functions

We might recognize a quadratic equation from the factoring chapter as a trinomial equation. Although, it may seem that they are the same, they aren’t the same. Trinomial equations are equations with any three terms. These terms can be any three terms where the degree of each term can vary. On the other hand, quadratic equations are equations with specific degrees on each term.

A quadratic equation is a polynomial equation of the form

$ax^2+bx+c=0,\nonumber$

where $$ax^2$$ is called the leading term, $$bx$$ is called the linear term, and $$c$$ is called the constant coefficient (or constant term). Additionally, $$a\neq 0$$.

In this chapter, we discuss quadratic equations and its applications. We learn three techniques for solving quadratic equations:

• Square root property
• Completing the square