Quadratic Formula

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:

Quadratic Formula

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.

Quadratic Formula Expanded

Derivation