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


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.



Adding xy to the first equation allows

us to see the parabolas in space. In

both cases the parabolas are moved

down 1 unit.