# Quadratic Formula

The Quadratic formula returns the x-intercepts of a quadratic equation. The formula is useful when the quadratic equation cannot be easily factored by hand. The result of the formula can be visualized as the roots or the x-intercepts of the equation which forms the shape of a parabola:

Plugging in the coefficients: a, b, and c of any quadratic equation into the formula will produce the x-coordinates of where the formula passes through the x-axis. Note, if the equation does not pass through the x-axis then there is no solution.

The first solution for x is given by the positive square root and the second solution for x is given by negative square root.

### Derive Quadratic Formula

To derive the quadratic formula, start with the general form of the quadratic equation set equal to zero and solve for the variable . The quadratic formula solves for the x-intercepts of the quadratic equation. The formula is especially useful when the quadratic equation is not easily factored.