how to find parabola function given a few points?

• Sep 1st 2012, 02:59 PM
potte
how to find parabola function given a few points?
I have a parabola, just need to find the function:
here are few points on the graph i traced
please, don't just give answer, I need to know how to do it. feels like i need the speed graph to figure out the parabola function but have no idea.(Thinking)
or you can give me the function and then tell me how you get it. much much appreciated. thanks in advance
x y
( 0 0)
 18 16 60 61 101 110 170 207 283 410 344 557 402 740
• Sep 1st 2012, 03:20 PM
MaxJasper
Re: how to find parabola function given a few points?
Use a regression method:
Least Square Method
• Sep 1st 2012, 11:42 PM
JJacquelin
Re: how to find parabola function given a few points?
Hi !

Of course, least squares fitting of the parabolic function y = c0*x2+c1*x+c2 will give you an approximate of your data.
But I suggest to perform both "absolute least squares" and "relative least squares" fittings. The coefficients c0, c1, c2 will be sligthly different. The first leads to a better Absolute Deviation, while the second leads to a better Relative Deviation. So you can chose the best on the physical point of view.