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

Explanation:

Step1: Identify the form of the quadratic function

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

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 to the right of the axis of symmetry. So the function $f(x)$ is decreasing for $x>-8$, which is the interval $(-8,\infty)$.

Answer:

A. $(-8,\infty)$