ax2 + bx + c = 0 is the equation of a parabola. The discriminant is b2 - 4ac, which you find in the quadratic formula:
x = [-b±√(b2-4ac)]/2a.
The discriminant shows you the type and number of solutions of the graph.
If b2 - 4ac > 0, the graph has two real solutions.
If b2 - 4ac = 0, the graph has one real solution.
If b2 - 4ac < 0, the graph has two imaginary solutions.