There is not much information given in this problem, nor is there any examples so I am lost.

Here is the problem:

Decide if it is possible for a parabola to have the indicated number of x-intercepts. If it is possible, find an equation of such a parabola. If not possible explain why.

a. One intercept

b. Three intercepts

The other part of the problem:

The vertex of a parabola is (5,3) and the parabola passes through the point (8,10). Find a third point that lies on the parabola?

I know that the vertex is the lowest point. Is there an equation that I would use to find the third point?