Answer
$-30$
Work Step by Step
General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$
Hence here: $\frac{f(7)-f(3)}{7-3}=\frac{(-3\cdot7^2+5)-(-3\cdot3^2+5)}{4}=\frac{(-147+5)-(-27+5)}{4}=\frac{-142-(-22)}{4}=\frac{-120}{4}=-30.$
