How are solutions, roots, and x-intercepts of a quadratic related?

A quadratic equation has the form ax2+bx+c=0 and is represented by a parabola (graphically). The solution of a quadratic equation is based on find the roots, which are the x-intercepts of its graph. When it has double root, the vertex of the parabola is the intercept with the x axis. If the root is imaginary (the discriminant of a quadratic function is negative), it does not intercept the x axis. So, a quadratic equation can has: one root, two roots, or zero roots.

You can solve a quadratic equation by factoring by applying a equation called "Quadratic formula", which is usually used when you can't factorize it. This formula is:

x = (-b±√ (b^2-4ac)) / 2a