You are right about the time spent learning how to use CAD will pay off in the future. I just like messing around with math (do some here at work) so I just wanted to see if I could use it for something useful. I took your advise for using an ellispe and starting with:

x^2/a + y^2/b = 1

came up with:

f(x) = (h^2 * (1 - [(x-w/2)/(w/2)]^2))^0.5

h = max height
w = max width
x = ranges from 0 to w

I have attached a plot with h = 2 and w = 3. Looks much better this time. Thanks folks!