In each of the previous examples, the

coefficient in front of

has been 1. But both the

vertex form,

, and the standard form,

, allow for the possibility of a different coefficient. Let’s explore different values in front of and see what happens to the graph.

Below is the basic

graph of

and several other graphs where the

coefficient in front of has been changed. Examine each

graph and see if you can tell what is happening.

A

coefficient larger than 1 will make the

graph more narrow. Sometimes this is explained as moving away from the x-axis. Now look at some other graphs.

When the

coefficient is between 0 and 1, the

graph becomes wider. Another way to say this is that it moves toward the x-axis.

We now need to look at what happens if the

coefficient is a negative number.

Whenever the

coefficient is a negative number, the

parabola will be reflected, or flipped over, the x–axis. If the

coefficient is negative and has a number, then you must

flip the

parabola and the make it more narrow or wider.