I require a math formula that lets me move smoothly between these graphs:
It must always intersect x=0 and x=1 as seen, and its peak must always be at 1. It can be a parametric equation. How might I generate something like this.
For example that middle graph might be equal to $y=-\left(2x-1\right)^{2}+1$
But that equation needs to somehow be modified to produce those other graphs.
Its almost like its interpolating between these 3 graphs:
A fit is given by $$y = \frac{x^{p}(1-x)^{1-p}}{p^p(1-p)^{1-p}}$$
with $$0<p<1$$
It can be checked at https://www.desmos.com/calculator/es1znohisl