Curve fitting points with a square root dependence

[jennyrabbit]

I have a data set , y as a function of x, which I can curve fit to be y = ax^2 + bx +c, but I would really like to have the explicit equation for x as a function of y. I tried just plotting x vs y and adding in a trendline, but Excel does not do curve fitting for anything but linear or polynomial. Does anyone have any suggestions? Thanks.

 

[jennyrabbit]

Thank you, Wizards, for your patience. I will try the various and sundry suggestions. And yes, I do persevere... ; )

 

[jennyrabbit]

A mystery indeed. If I take this data set
cgs grams/sec
0 0
137.8956035 0.0464
482.6346124 0.07076
1103.164828 0.0812
1999.486251 0.11716
3171.598881 0.145
4550.554917 0.1624
5998.458754 0.1856
8066.892807 0.2204
10066.37906 0.24708
12341.65652 0.2784
14961.67298 0.3016
21718.55756 0.3538
28751.23334 0.4176
37507.60416 0.47154
48677.14805 0.5336
61639.33478 0.5916
76601.00776 0.6612

and do a fit to a1*x^e1, I at first only got a fit with the exponent of -0.6. I went home in frustration and tried it again, and this time got a decent fit with a positive exponent. The fit wasn't perfect, though, so I tried a fit using a1*x^e1 + a2*x^e2, and the fit was worse than the first fit, AND I got this nasty negative exponent in e2. The solver seems to be flakey, and I'm wondering if anyone else has had a solver give weird, irreproducible results, or results that make no sense. Any guidance on this much appreciated.