contents

Introduction and Summary

This chapter deals with equations involving quadratic polynomials, i.e. polynomials of degree two. Quadratic equations are equations of the form y = ax 2 + bx + c or y = a(x - h)2 + k .

The shape of the graph of a quadratic equation is a parabola. The first section of this chapter explains how to graph any quadratic equation of the form y = a(x - h)2 + k , and it shows how varying the constants a , h , and k stretches and shifts the graph of the parabola.

The second section revisits factoring. In the last chapter, we learned how to factor expressions. Here, we factor equations of the form x 2 + bx + c = 0 , splitting the expression into two binomials and using the zero product property to solve the equation.

Not all equations ax 2 + bx + c = 0 can be easily factored. Thus, we need a formula to solve for x . This is the quadratic formula, and it is the focus of section three.

Finally, in the last section, we learn how to graph quadratic equations of the form y = ax 2 + bx + c by completing the square: adding and subtracting a constant to create a perfect square trinomial within our equation.

Though quadratic equations are just one type of polynomial, they are studied more in Algebra I and II than all other types of polynomials. They have unique properties that fascinate mathematicians, and they can be used as a model to understand more complex polynomials.

Take a Study Break

Star Trek gets SEXY

Chris Pine and Zoe Saldana heat up the red carpet!

Are you afraid of relationships?

Auntie SparkNotes can help!

Sexy starlet style

See every single look from the Met Gala!

Geeky Actors: Then and Now

Travel back in time!

Villains We Want These Actresses to Play

From super cute to super bad!

10 Movies Better Than Their Books

What do you think?

How To Look Like J-Law...

When you don't look like J-Law.

12 Scientific Inaccuracies in Into Darkness

What did Star Trek get wrong?

The Book

Read What You Love, Anywhere You Like

Get Our FREE NOOK Reading Apps