The following data points are expected to follow a functional variation of $y=a{x}^2+bx+c.$ Obtain the values of $a,b,$ and $c$ by the method of least squares $($Quadratic Regression$).$ Plot the data points and the resulting curve using any available software $($Excel$,$ MathCAD, Matlab, etc.$)$

$\backslash$table$[[x,1\mathrm{.}21,1\mathrm{.}35,2\mathrm{.}40,2\mathrm{.}75,4\mathrm{.}50,5\mathrm{.}10,7\mathrm{.}10,8\mathrm{.}10],[y,1\mathrm{.}20,1\mathrm{.}82,5\mathrm{.}00,8\mathrm{.}80,19\mathrm{.}5,32\mathrm{.}5,55\mathrm{.}0,80\mathrm{.}0]]$