Question

over what interval is the graph of $f(x) = -(x + 8)^2 - 1$ decreasing?
$\bigcirc$ $(-8, \infty)$
$\bigcirc$ $(8, \infty)$
$\bigcirc$ $(-\infty, 8)$
$\bigcirc$ $(-\infty, -8)$

Explanation:

Step1: Identify vertex form

The function is $f(x)=-(x+8)^2-1$, vertex form $f(x)=a(x-h)^2+k$.
Here, $a=-1$, $h=-8$, $k=-1$.

Step2: Determine parabola direction

Since $a=-1<0$, parabola opens downward.

Step3: Find decreasing interval

Downward parabola decreases to the right of vertex $x=h=-8$.
Interval: $(-8, \infty)$

Answer:

$(-8, \infty)$