I presume that "x-axis values of -3 and 5" means these are the x intercepts (-3, 0) and (5, 0)?

Then

is as good as you are going to get with the current information. The only thing you can do with it now is to find the axis of symmetry, which is supposed to be the line x = 1. But:

has an axis of symmtry at

and the "a" cancels out naturally. So we have no new information here.

What is the significance of the graph of ?

-Dan