The graph of an equation with a negative discriminant always has which characteristic?

The graph does not intercept the x-axis

Step-by-step explanation:

Hi there!

When the discriminant is positive, it means that in the quadratic equation, you can take the square root of this number and end up with two distinct solutions, one negative and one positive. The graph will intercept the x-axis twice.

When the discriminant is zero, it means that you won't be taking the square root of any number in the quadratic equation and you'll end up with two solutions that are equal, or just one distinct solution. The graph will intercept the x-axis once.

When the discriminant is negative, it means that the quadratic has no real solutions, meaning that it does not intercept the x-axis. It is impossible to take the square root of a negative number.

I hope this helps!