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

Answer:

A. $(-8,\infty)$

Explanation:

Step1: Identify the function form

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

Step2: Analyze the sign of $a$

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

Step3: Determine the vertex

The vertex of the parabola is $(h,k)=(-8,-1)$.

Step4: Find the decreasing interval

For a parabola that opens downwards, the function is decreasing to the right of the vertex. So the function $f(x)$ is decreasing for $x>-8$, which is the interval $(-8,\infty)$.