Valerie Russell

Exploring a

Let's see what happens as a increases or decreases.

 As a increases the parabola stretches creating a narrower parabola

 Likewise, as a decreases the parabola shrinks creating a broader parabola.

So far we have seen that if the leading coefficient a is positive the quadratic function called a parabola opens upward and if the leading coefficient is negative the parabola opens downward. As a increases the parabola stretches and as a decreases the parabola shrinks.

Exploring b

Exploring c

 Notice that as c increases the parabola moves upward. As c decreases the parabola moves downward.

Did you know that you can easily see where the vertex and axis of symmetry lie in a quadratic equation when it is in vertex form? You can change the standard form of a quadratic equation to vertex form by using a method called completing the square. Let's take a look at several quadratic equations in vertex form.

 The coefficient of the quadratic equation a causes the parabola to shrink as a decreases and stretch vertically as a increases.

Extensions:

 Adding xy to the first equation allows us to see the parabolas in space. In both cases the parabolas are moved down 1 unit.