Answer
(a) $-2$
(b) $0$
(c) $5$
Work Step by Step
Given $h(x)=x^2-2x+3$, we have the average rate of change
$R=\dfrac{h(x_2)-h(x_1)}{x_2-x_1}$
(a) From $x_1=-1$ to $x_2=1$, we have
$R=\dfrac{h(1)-h(-1)}{1-(-1)}=\dfrac{(1)^2-2(1)+3-[(-1)^2-2(-1)+3]}{2}=-2$
(b) From $x_1=0$ to $x_2=2$, we have
$R=\dfrac{h(2)-h(0)}{2-0}=\dfrac{(2)^2-2(2)+3-[(0)^2-2(0)+3]}{2}=0$
(c) From $x_1=2$ to $x_2=5$, we have
$R=\dfrac{h(5)-h(2)}{5-2}=\dfrac{(5)^2-2(5)+3-[(2)^2-2(2)+3]}{3}=5$
