I have a horrible memory. I don’t mean just that I misplace things or forget names; it takes a *lot* of effort to commit arbitrary facts, figures, dates, etc., to my long-term memory. So throughout my school years, most of my studying was for things like History, trying hard to remember dates and statistics that I would quickly eject from my mind after my next exam. I seldom had to study for Math or Science though, because I figured out something that worked for me there: learning *how* and *why* things work rather than just memorizing formulas. This worked well for those subjects, but I do remember stumbling in algebra when I was not able to factor quadratic functions. There was a handy Swiss army knife of sorts for this, of course, in the Quadratic Formula.

I avoided this formula as much as possible, usually by spending *way* too much time trying to guess the factors myself, or by converting from “standard form” to “vertex form”, or guessing, or skipping that question. This was almost entirely because I could not bring myself to memorize the formula. Call it laziness, or foolishness, or whatever you’d like.

Well, recently I decided to brush up on my math skills. After yet again encountering the need for this equation, I decided enough is enough. Since I can’t memorize the equation, I will instead learn where it comes from by *deriving* it from the standard form of a quadratic function. This is my attempt to do so.

Continue reading Quadratic Confusion