Animated Mathematics

The Quadratic formula

The quadratic formula is often presented as a "magic" formula, which is given without proof to find the solutions of any quadratic equation. The derivation of this formula is usually percieved as being too difficult, and only for the advanced student. I concede that the derivation can be difficult to follows when first encountered, since the equations only contains symbols and no numbers. However, the derivation can become accessible to the majority of students with the use of diagrams to visually explain the completing the square of the general form of the quadratic equation:

Before continuing with the derivation we shall go over the last two algebraic steps visually:

The formulas looks formidable but we are nearly there, read on:


We have derived the quadratic formula and in the next we shall use the quadratic formula to find the solutions. The derivation looks intimidating, but don't worry even straight A students find it challenging when they first encounter it. With practice C students can become B students, B students can become A students, F students can become E students, and so on.