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


  1. Divide both sides by .

  2. Subtract from both sides.

  3. Add to both sides to prepare to factor the left side by completing the square.

  4. Factor the left side and simplify the right side by combining the fractions.

  5. Take the square root of both sides.

  6. Subtract from both sides and solve for .

  7. Quadratic Formula.