Fit a Quadratic Curve to Data I have some data and I want to fit a quadratic curve for my data But I don't know that how to it do? 
My data :
$x,y = 100,45;$ 
$x_1,y_1= 101, 50$;
$x_2,y_3=99,35$;
$\ldots$
For instance this website is fitting function very well http://mycurvefit.com/
But I don't know how ıt is work?What is the background?
How can I calculate mathematical way this function?
Thank your advanced
 A: So you want to fit your given points with the curve $
f(x) = a + b\,x + c\,x^{\,2} $. There are many "fitting" methods to choose from depending on considering the nature of the data and of the underlying error. I suppose you refer to the most common "least square" method (in the most common acception which assumes that the error is just on the $y$ coordinate).
Then the underlying mechanism of it is to calculate the total square error $$
E(a,b,c)^{\,2}  = \sum\limits_k {\left( {y_{\,k}  - f(x_{\,k} )} \right)^{\,2} }  = \sum\limits_k {\left( {y_{\,k}  - a - b\,x_{\,k}  - c\,x_{\,k} ^{\,2} } \right)^{\,2} } 
$$
which depends on the unknown parameters $a,b,c$ and find for which value of them it becomes minimum. So (under proper assumptions concerning the data distribution ...which practically are assessed from a plot of the data) you are to solve the system
$$
\left\{ \matrix{
  0 = {\partial  \over {\partial \,a}}E(a,b,c)^{\,2}  =  - 2\sum\limits_k {\left( {y_{\,k}  - a - b\,x_{\,k}  - c\,x_{\,k} ^{\,2} } \right)}  \hfill \cr 
  0 = {\partial  \over {\partial \,b}}E(a,b,c)^{\,2}  =  - 2\sum\limits_k {x_{\,k} \left( {y_{\,k}  - a - b\,x_{\,k}  - c\,x_{\,k} ^{\,2} } \right)}  \hfill \cr 
  0 = {\partial  \over {\partial \,c}}E(a,b,c)^{\,2}  =  - 2\sum\limits_k {x_{\,k} ^{\,2} \left( {y_{\,k}  - a - b\,x_{\,k}  - c\,x_{\,k} ^{\,2} } \right)}  \hfill \cr}  \right.
$$
This is finally a linear system in the unknowns $a,b,c$ which provides the solution, always given that the data distribution be actually "nearly quadratic".  
