What can you tell about the graph of a quadratic function based on the roots you get from solving the quadratic formula for that equation?

When using the quadratic formula to solve for the roots of a quadratic function, you will be able to tell if the quadratic has two real roots with different intercept points, two real roots with one point, or two complex, or non-real, roots.

Using the discriminant, you can determine this even quicker than with using the quadratic formula. If the discriminant works out to be greater than zero, your quadratic will have two real roots. If the discriminant works out to be equal to zero, it will have two real roots that are equal to each other, and if the discriminant is less than zero, it will have two complex roots.