Given the formula for a parabola in vertex form: $y = a(x-h)^2+k$, as $h$ and $k$ are changed, the $a$ value will adjust in order to keep the left hand $x$-intercept anchored to the origin. I'm really only interested in quadrant $I$, and between $0 ≤ x,y ≤ 1$.
What I'm really looking to do is graph a curve (the type is negotiable) that rises from $(0, 0)$, peaks at some target/adjustable number near $(0.5, 1)$, and then falls, depending on where the peak is, to $(1, 0)$.
I considered using a spline for this, but this curve will drive a function in an inefficient node based system, where I need to keep the math complexity is low as possible. A parabola seems like the best fit.