Nice site, but it makes a meal out of the material. The technique of 'completing the square' is about as quick and easy as the quadratic formula (indeed, doing it with generic coefficients is what gives you the quadratic formula) and only calls on a good elementary understanding rather than dredging up a formula from the memory banks.
I think among the first things they taught us when I took physics at university was to forget about the formula, and learn to complete the square. Felt they had a fairly low opinion of the education we had been given thus far, so we had to do it almost as a kata to prepare for the reality of actually needing to rely on algebra abilities.
This was followed by years of professors telling us to learn to derive all sorts of formulas and identities rather than to memorize them.
Learning to derive a formula creates a sort mathematical self-sufficiency that you don't get when you memorize a formula.
