Numerical Methods20805 marksNumerical: Polynomial curve fittingQuadratic polynomial fitting
Fit a second order polynomial to the data in the table below:
Fit a second order polynomial to the data in the table below:
$$\begin{array}{|c|c|c|c|c|c|}\hline X & 1 & 2 & 3 & 4 & 5 \ \hline F(x) & 2 & 6 & 12 & 20 & 30 \ \hline \end{array}$$
[5]
X 1 2 3 4 5 ------------------ f(X) 2 6 12 20 30 Model: $f(x) = a0 + a1 x + a2 x^2$, with $n = 5$. x f x² x³ x⁴ xf x²f --------------------------- 1 2 1 1 1 2 2 2 6 4 8 16 12 24 3 12 9 27 81 36 108 4 20 16 64 256 80 320 5 30 25 125 625 150 750 Σ 70 55 225 979 280 1204