We are tasked with finding the average rate of change of the function $f(x) = -x^2 - 8x + 21$ over the interval $[-10, 0]$.

The average rate of change of a function over an interval $[a, b]$ is given by the formula:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$

For this problem:

• The function is $f(x) = -x^2 - 8x + 21$
• The interval is $[-10, 0]$, so $a = -10$ and $b = 0$

Step 1: Calculate $f(-10)$