Describe how to derive the quadratic formula from a quadratic equation in standard form.

Answer:

To derive the quadratic formula, start with the standard form of a quadratic equation, ax^2 + bx + c = 0. Divide the entire equation by a, then move the constant term c to the other side. Complete the square by adding (b/2a)^2 to both sides of the equation. This allows you to factor the left side as a perfect square trinomial. Finally, take the square root of both sides and isolate x to arrive at the quadratic formula.