Chapter 7.5, Problem 21E

To find the coefficients of the parabola

     $y=a{x}^2+bx+c$

that is the “best” fit to the points (1, 2), (2, 1), (3, 1), and (4, 3), minimize the sum of the squares of the residuals

     $\begin{array}{ccc}F\left(a,b,c\right)& =& {\left(a+b+c-2\right)}^2\\ & & +{(4a+2b+c-1)}^2\\ & & +{(9a+3b+c-1)}^2\\ & & +{(16a+4b+c-3)}^2\end{array}$

by solving the system of normal equations

   $\begin{array}{ccc}{F}_a(a,b,c)=0& F_b\left(a,b,c\right)=0& F_c\end{array}\left(a,b,c\right)=0$

for a, b, and c. Graph the points and the parabola.