In each of the previous examples, the coefficient
in front of
has been 1. But both the vertex
, 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
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.
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
and the make it more narrow or wider.