Consider the function $f(x)=8(x-1{)}^2$ on the interval $0,2.$

$($a$)$ Sketch the function on the axes provided.

$($b$)$ Shade the region whose area is defined as ${\displaystyle \underset{0}{\overset{2}{}}}8(x-1{)}^{2}dx$

$($c$)$ Draw the rectangles you would use to calculate $M_4,$ the midpoint approximation using $4$ rectangles. Then find the value of $M_4.$