### Learning Outcomes

By the end of this section, you will be able to:

- Graph quadratic functions using tables and transformations
- Identify important features of the graph of a quadratic function of the form [latex]f(x)=ax^2+bx+c[/latex]

Quadratic functions are especially helpful for modeling real-world situations where a minimum or maximum function value would help solve a problem. They are used to answer questions in business, physics, engineering, and more, such as

- What maximum height does a projectile achieve before falling back to the ground and how long after launch will it land?
- What price should be applied to a cup of coffee to maximize revenue?
- What number of units should a factory produce each day to minimize costs?

Before studying problems such as these, though, it is necessary to define the characteristics of the function and learn what they reveal about the model. You’ll need an understanding of the vertex and intercepts (real and complex), different algebraic forms of the quadratic function, and some formulas for quickly identifying certain features.

In preparation for studying these functions, take a close look in this review section at the shape of the graph of the function and how it can be used to describe projectile motion in the plane.

Warm up for this module by refreshing important concepts and skills you’ll need for success. As you study these review topics, recall that you can also return to Algebra Essentials any time you need to refresh the basics.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.