Hi there!
[tex]\large\boxed{\text{Average rate = 1}}[/tex]
We can calculate the average rate of change using the following:
[tex]ARC = \frac{f(b)-f(a)}{b-a}[/tex]
Thus, we can plug in the endpoints of -4 and -2. Find the corresponding y-values for these x-values:
f(-2) = -(-2)² - 5(-2) + 8 = -4 + 10 + 8 = 14
f(-4) = -(-4)² - 5(-4) + 8 = -16 + 20 + 8 = 12
Plug in the solved for values into the ARC equation:
[tex]ARC(slope) = \frac{14-12}{-2(-4)} = \frac{2}{2} = 1[/tex]
