The values of $x$ that solve the quadratic equation,

\( \large 0=ax^2 + bx + c, \)

are given by the quadratic formula,

\( \Large \frac{-b\pm\sqrt{b^2-4ac}}{2a}. \)

If the discriminant $D=b^2-4ac$ is greater than zero, the argument of the square root is positive and the parabola $y=ax^2 + bx + c$ crosses the $y=0$ axis at two points. If $D=0$, the parabola touches the $y=0$ axis at one point. If $D<0$, the parabola does not cross the $y=0$ axis.