The General Quadratic Equation Formula

Benefits of showing where the formula comes from

I often show my student how the formula for solving a general quadratic equation is derived. This, understandably, seems quite complex to them. The benefits of showing them the development of the formula in full detail are:

1) After that, memorizing the formula seems an easier task in comparison.
2) Plugging in the correct values in the formula and evaluating it to a numerical result seems now way easier than having to figure out the solutions for each particular equation by completing the square. The fact that the formula is available saves them the work of completing the square in each particular case.
3) They now have seen how the formula is developed. Even if they do not understand the process 100%, even if they forget the process within five minutes, the formula itself is no longer a mystery. They know there is an algebraic derivation of it, and they have seen it, at least once. They feel now much more confident in using the formula.

So, because of the previous reasons, it is totally worth it to go through the process of showing them how the formula is developed. It is time well invested.