I help some help please.

Basically if i had a graph of e.g.

y=-(x-3)^2+1

I know that my graph would intersect the x-axis at x=2 and x=4.

However if I didn't know the equation of my curve, but knew the shape of the graph was like y=-(x-3)^2+1, and it crossed the x-axis at 2 points.

How could I prove that it had 2 roots?

I think I may have something to do with continuity, but not sure.

Any help is appreciated.