# Can I do reverse curve fitting operation of 2nd order curve y=a+bx+cx^2?

I have data points of x[i] and y[i] where x is independent variable.And,I can model these points as nth order polynomial using any regression analysis.I am doing 2nd order polynomial curve fitting that has the best fit to a series of my data points.Now,from these 2nd order fitted curve,can I get my original data points set in any way?

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• Why does the adjective "reverse" mean in this case? You can do a least squares fit to solve for the coefficients a, b, and c for more than 3 points. You can solve it for exactly three points. What's the question? – duffymo Feb 25 '14 at 12:28
• I have a curve f(x) and I will get y=a+(bx)+(c*x^2) after doing 2nd order curve fitting on f(x).Is it possible to get f(x) back?By doing reverse operation of curve fitting? – user91797 Feb 25 '14 at 12:33
• Unless f(x) == a+b(x)+c*x^2 the answer is no. – Azrael3000 Feb 25 '14 at 12:35
• Sorry, this makes no sense to me at all. "I have a curve f(x)" - why do you need to fit a quadratic, then? What is the curve f(x) for - generating points for the fit? – duffymo Feb 25 '14 at 12:44
• Sorry,Let me explain my problem like this.I have data points of x[i] and y[i] where x is independent variable.And,I can model these points as nth order polynomial using any regression analysis.I am doing 2nd order polynomial curve fitting that has the best fit to a series of my data points.Now,from these 2nd order fitted curve,can I get my original data points set in any way? – user91797 Feb 25 '14 at 12:49