Question

how do you know what graph has a discriminant of zero?

Answer 1

If it is tangent to the graph.

Answer 2

if all you have is a graph; the graph will only touch the x axis in one spot then curve back

Answer 3

If it is tangent, then that means it has a discriminant of zero. By the way, if it intersects at two points, that means it has a discriminant larger than 0, and if it does not intersect, that mans it has a discriminant smaller than 0.