Hey, BOGWarrior89 here, just like to say I'm out of high school and going into a college mathematics major program (alongside another major in physics). I took a semester of Pre-Calculus and Trigonometry, other than that, not much more to say on that subject.
My current "work" is on the quadratic formula (I had a problem with solving asymptotes using "x approaches infinity" limits). Unfortunately, I don't have my notebook with me, but I can try to recall it offhand. I seriously need an opinion on this, so here goes (new variables in bold):
" y = ax^2 + bx + c" -> " x = ( -b +- [ b^2 + 4ay - 4ac ]^1/2)/(2a) "
" y = ( ax^2 + bx + c )/( dx + e ) " -> " x = ( -b + dy +- [ b^2 + (d^2)(y^2) + 4aey - 2bdy - 4ac]^1/2)/(2a)"
" y = ( ax^2 + bx + c )/( fx^2 + dx + e ) " -> " x = ( -b + dy +- [ b^2 + (d^2)(y^2) + 4fey^2 + 4aey - 4cfy - 2bdy - 4ac]^1/2)/(2a - 2fy)"
The best part? If "y = 0", then the outcome for all three of these is the original quadratic formula.
I'm hoping I can post a picture of the real thing; it's easier to read. Tell me what you think.