Question

quadratic functions: vertex form over what interval is the graph of $f(x) = -(x + 8)^2 - 1$ decreasing? $(-8, infty)$ $(8, infty)$ $(-infty, -8)$ $(-infty, 8)$

Explanation:

Step1: Analyze the quadratic function's form

The function is given in vertex form \( f(x)=a(x - h)^2 + k \), where \( a=-1 \), \( h=-8 \), and \( k = - 1 \). The vertex is at \( (h,k)=(-8,-1) \). Since \( a=-1<0 \), the parabola opens downward.

Step2: Determine the interval of decrease

For a parabola that opens downward, the function is decreasing to the right of the vertex's x - coordinate. The x - coordinate of the vertex is \( x=-8 \). So the function \( f(x) \) is decreasing for \( x>-8 \), which is the interval \( (-8,\infty) \).

Answer:

\((-8,\infty)\)