How can I create a quadratic equation that best fits 11 points of data. The 11 points are (4, 3.1), (5, 4.74), (6, 6.13), (7, 7.26), (8, 8.14), (9, 8.77), (10, 9.14), (11, 9.26), (12, 9.13), (13, 8.74), and (14, 8.1). Now I don't expect anybody to tell me what this equation comes out to because it is estimated that such will come out to 15+ pages. I am asking how one determines the equation that best fits any three points in english. By understanding this, I feel that I could possibly create the 11-point equation myself.

http://smackaay.com/2009/04/29/3-point-quadratic-regression-formula/
The above site shows how to find a,b and c in plain english. I am not how one goes about in process to figure such equation out. Is there anybody that can give me any help or provide me with some resources to go about learning how to do such, it would be greatly appreciated. The author apparently used backwards gaussian analysis and simplification through mathematica to produce the equation in english. I would like to do such for 11 points in plain english.

The reason I do not want to use a computer or calculator to compute the equation for me is that I will not learn the inference suggested by the regression. Again, f anybody can help me here, it would be greatly appreciated.

John