Answer
$a.\quad-4$
$b.\quad-8$
$c.\quad-10$
Work Step by Step
Average rate of change from $a$ to $b$
$=\displaystyle \frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b-a},\quad a\neq b$
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$a.$
$f(2)=-2(2)^{2}+4=-4$
$f(0)=-2(0)^{2}+4=4$
$\displaystyle \frac{f(2)-f(0)}{2-0}=\frac{(-4)-(4)}{2}=\frac{-8}{2}=-4$
$b.$
$f(3)=-2(3)^{2}+4=-14$
$f(1)=-2(1)^{2}+4=2$
$\displaystyle \frac{f(3)-f(1)}{3-1}=\frac{(-14)-(2)}{2}=\frac{-16}{2}=-8$
$c.$
$f(4)=-2(4)^{2}+4=-28$
$f(1)=-2(1)^{2}+4=2$
$\displaystyle \frac{f(3)-f(1)}{4-1}=\frac{(-28)-(2)}{3}=\frac{-30}{3}=-10$
