The quadratic formula is used to find the x-intercepts of a quadratic equation that cannot be factored. It is in the form x = (-b ± √(b2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. You substitute the coefficients for a, b, and c, simplify within the radical, and solve the equation twice - once with addition in the radical and once with subtraction - to find the two x-intercepts.