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 parabola vertex form

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

Step2: Determine parabola direction

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

Step3: Find decreasing interval

A downward-opening parabola decreases to the right of its vertex $x=h=-8$. So the interval is $(-8, \infty)$.

Answer:

$(-8, \infty)$