In many ways, this is more a general maths question than an excel question, but have always gotten good answers here so figured I would try.

I am trying to model the shape of a curve, based on several data points that I have. However, the data points are not in a format immediately useful to excel.

Specifically, I have the following data points for the curve. Roughly speaking, the curve is an upside down parabola.

(X,Y) start point is 0,0 by definition

I then have the X end point (130)

I have the Y maximum value (500)

Finally, I have the X value of when the Y value is at it's peak (50)

Area under the curve (220)

So I have 3 points only for the curve: (0,0), (50,500), (130,0).

Turning these 3 into a curve doesn't reflect the area under the curve, which is something I would like to do. So, my question, is how to derive a formula for the curve which both passes through the 3 points, but also has the correct area.

Visually, I see this as being an adjustment to the curvature either side of the peak point, either making it more like a triangle, or less so. In terms of assumptions, I am assuming no inflection points.

For reference, I have ~600 of these curves to model, so a formula driven approach is a must.

Thanks!