Numerical Methods05 marksNumerical: Quadratic curve fittingQuadratic polynomial fitting
Fit the quadratic curve through the following data points and estimate the value of f(x) at x=2.
Fit the quadratic curve through the following data points and estimate the value of f(x) at x=2.
$$\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 3 & 4 & 5 & 6 \ \hline y & 2 & 7 & 8 & 7 & 5 \ \hline \end{array}$$
[5]
$x$ 1 3 4 5 6 -------------------- $y$ 2 7 8 7 5 $n = 5$. Fit $y = a0 + a1 x + a2 x^2$, estimate $f(2)$. $x$ $y$ $x^2$ $x^3$ $x^4$ $xy$ $x^2y$ --------------------------------------------- 1 2 1 1 1 2 2 3 7 9 27 81 21 63 4 8 16 64 256 32 128 5 7 25 125 625 35 175 6 5 36 216 1296 30 180 Totals: - ...