### Learning Outcomes

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

- Complete the square to form perfect square trinomials

This module looks at geometric objects: the ellipse, the hyperbola, and the parabola. You have seen a parabola before. It is the shape formed in the real plane by a second-degree polynomial in two variables, the quadratic. In this module, though, you’ll explore its geometric characteristics along with those of the other conic sections. You’ll encounter a slightly different form of the equation for a parabola than you’ve seen before and you’ll see that they can open left and right as well as up and down. Since the conic sections are geometric objects, their graphs are not limited to function characteristics.

A key algebraic feature involved in writing the equation of conic sections is the technique of completing the square to write a perfect square trinomial. You last saw this method in the text when solving quadratic equations, so a refresher is probably in order. Practice the skill before beginning this module to help reduce the challenge in upcoming examples and practice problems.

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.