LetÕs
begin this investigation by looking at several graphs of **y = aX ^{2}**, with varying values of

If we look specifically at the graphs of y= 5x^{2} and y=-5x^{2} as compared to y= x^{2} we can readily see the
distinction between y= 5x^{2 }and y=-5x^{2}. The graph of y=5x^{2}
opens concave upwards while the graph of y=-5x^{2}
opens concave downwards or we can simply say that y=-5x^{2}
is y= 5x^{2 }reflected over the x-axis.

We must also compare these graphs to the graph of y= x^{2}. Here we can see that the graphs of y=
5x^{2 }and y=-5x^{2} are
more narrow than the graph of y= x^{2}. This is a dilation, more specifically a
vertical expansion of y= x^{2}.

Notice that the graph becomes steeper (more narrow) when **a** is increased to 5. As **a** increases the graph
continues to become steeper, hence the term vertical expansion.

Here we see the graph becomes wider for **0 < a <1**. This is called a vertical compression
because the graph is wider and shorter.