Give to an interpolation function an analitic function with mathematica

[UNKNOWN089]

i have solved a differential equation with shooting methods, the output is in form of interpolate function, i can see it with a graphics, but i i would have an approssimate analitic form what kind of function i have to do ?

the equation give in output have this form..

InterpolatingFunction[{{-0.35,0.35}},<>][theta1]

where theta1 is the indipendet variable...
i would like to have a forme like :

g[theta1] = a *theta1^2+ b*theta1+ c...

how can i have this solution ?

 

[K.J.Healey]

Use "FindFit"