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.

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