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

Explanation:

Step1: Identify the function type

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 axis of symmetry

The axis of symmetry of a quadratic function in the form $y=a(x - h)^2+k$ is $x = h$. Here, the axis of symmetry is $x=-8$.

Step4: Find the decreasing interval

For a parabola that opens downwards, the function is decreasing on the interval $(-\infty,h)$. So, for $f(x)=-(x + 8)^2-1$, the function is decreasing on the interval $(-8,\infty)$.

Answer:

$( - 8,\infty)$