I don't think so. I was on the Calculus track in high school so we derived it in...Pre-Calculus.
Prior to that the quadratic formula was something that seemed to be handed down from on high. We used it in Algebra II and maybe even before that, but I had no idea where it came from.
It was a mind-opening experience when we derived it in class one day. Our teacher didn't ruin the surprise. She just said, let's complete the square on a general quadratic equation. And there it was. The quadratic formula!
> Our teacher didn't ruin the surprise. She just said, let's complete the square on a general quadratic equation.
How is this not ruining the surprise? The only possible outcomes of doing that are that (1) you make a mistake; or (2) you get a formula for solving quadratic equations. Quadratic equations have the same solutions regardless of your methodology, so there's only one formula you can get.
Prior to that the quadratic formula was something that seemed to be handed down from on high. We used it in Algebra II and maybe even before that, but I had no idea where it came from.
It was a mind-opening experience when we derived it in class one day. Our teacher didn't ruin the surprise. She just said, let's complete the square on a general quadratic equation. And there it was. The quadratic formula!