In the diagram, x runs from 0 to 100 and y runs from 0 to 100. These represent percentages. So, looking at the diagram, for the uppermost curve at x=25%, y=80% while the lowermost curve is showing that at x=25%, y=50%. Since these curves represent percentages, the y value can never exceed 100. The points (0,0) and (100,100) are fixed points. You can't use a 3 point curve fit where the (25,80) point or (25,50) is the intermediate point, since such a polynomial will generate a parabola whose height exceeds 100. This curve looks more like part of a hyperbola or an arctan function of some sort.

Can anyone give me an idea of how I might find such an equation.