The discriminant from Algebra returns, particularly the Discriminant and the Plane. Recall that the descriminant is the $b^2 - 4ac$ part of the quadratic equation (see below):

$$\frac{-b \pm \sqrt{b^2 -4ac}}{2a}$$

Three Things Can Happen

Number 1: If the discriminant is positive, the equation has two $x$-intercepts and will cross the $x$-axis twice.

Number 2: If the discriminant is $0$, the equation has exactly one $x$-intercept and will intersect the $x-axis$ once.

Number 3: If the discriminant is negative, the equation has zero $x$-intercepts and will NOT cross the $x$-axis at all.