over what interval is the graph of $f(x)=-(x + 8)^2-1$ decreasing?\n(-8, ∞)\n(8, ∞)\n(-∞, 8)\n(-∞, -8)
over what interval is the graph of $f(x)=-(x + 8)^2-1$ decreasing?\n(-8, ∞)\n(8, ∞)\n(-∞, 8)\n(-∞, -8)
Answer
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 $a=-1$, $h=-8$, and $k = - 1$.
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 is decreasing for $x>-8$, which is the interval $(-8,\infty)$.
Answer:
A. $(-8,\infty)$