Question

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

Explanation:

Step1: Identify the vertex form

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

Step2: Determine the direction of opening

Since \( a=-1<0 \), the parabola opens downward.

Step3: Find the interval of decrease

For a downward - opening parabola \( y = a(x - h)^2 + k \) (\( a<0 \)), the function is decreasing on the interval \( (h,\infty) \). Here, \( h=-8 \), so the function is decreasing on the interval \( (-8,\infty) \).

Answer:

\( (-8,\infty) \) (corresponding to the first option: \( (-8,\infty) \))