I dissected 2nd degree polynomial functions using the Genius Curve Fitting program (free version). This is what I found: y = ax^2 + bx + c Given points (0, 2), (1, 3), and (2, 10)... a = y2 - ((y2-y0) / 2) - y1 b = y1 - a c = y0 Using these rules, the equation becomes: y = 3x^2 - 2x + 2 The rules certainly apply whenever xn = n. For other intervals of x, there will be some modifying of the equation that is necessary. Now my question is, how do I generate a function for a polynomial of the 3rd degree, 4th degree, and so on? The free version of Genius Curve Fitting only allows up to three points to be plotted, so I am unable to figure anything out.
My guess would be using matrices and then transforming it into reduced row-echelon form. I'll give an example for the third degree polynomial you posted. We start by inserting the points into the matrix. Code (Text): [[0 0 1 | 2 ] [1 1 1 | 3 ] [4 2 1 | 10]] Then we transform it into reduced row-echelon form. Code (Text): [[1 0 0 | 3 ] [0 1 0 | -2] [0 0 1 | 2 ]] Now we can just read the results from the matrix. This should also apply to polynomials of any degree.
