Answer
Net change: $h^2+2h$
Avg. rate of change: $h+2$
Work Step by Step
Net change:
$f(b)-f(a)=$
$f(2+h)-f(2)=$
$(2+h)^2-2(2+h)-(2^2-2(2))=$
$4+4h+h^2-(4+2h)-(4-4)=$
$4+4h+h^2-4-2h=$
$h^2+2h$
Avg. rate of change:
$\frac{f(b)-f(a)}{b-a}$
$f(b)-f(a)$ was already found above, so:
$\frac{h^2+2h}{2+h-2}=$
$\frac{h(h+2)}{h}=$
$h+2$