How to find the best polynomial that fits the following function!

Question

This is actually my first question in the math forum. I am trying to duplicate the attached polynomial using as fewer points as I could see picture 1. Furthermore, I need also to control the curvature such that P1 (moves up and down) is a movable point and P2 is a fixed point see picture 2.

Orginal Polynomial

Schematic diagram of the required

The point distribution of the polynomial are as below;

x       y
0.005   44.81839716
0.028   43.82844733
0.059   41.30393108
0.083   37.9860759
0.114   31.80662588
0.138   27.60547091
0.169   22.97499314
0.200   19.16200589
0.231   16.11724316
0.255   14.25948199
0.307   11.35062076
0.333   10.36567635
0.357   9.57967646
0.396   8.504148089
0.419   8.013775773
0.435   7.742658941

I fitted a fifth order polynomial, however, it required defining 6 points. What would be the smartest way to duplicate it and control the curvature as illustrated in the picture 2. Any help or advice would be greatly appreciated.

Thanks for your time.