What is the relationship between the discriminant and graph

Question

What is the relationship between the discriminant of ax2 + bx + c = 0 and the graph of y=ax² + bx + c

Answer 1

Taking off on Carol H.'s answer

if the discriminate > 0, the graph intersects the abscissa twice

if the discriminate = 0, the graph intersects (touches) the abscissa once

if the discriminate < 0, the graph does not intersect the abscissa. 

Answer 2

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.