QuestionApril 20, 2025

Over what interval is the graph of f(x)=-(x+8)^2-1 decreasing? (-8,infty ) (8,infty ) (-infty ,8) (-infty ,-8)

Over what interval is the graph of f(x)=-(x+8)^2-1 decreasing? (-8,infty ) (8,infty ) (-infty ,8) (-infty ,-8)
Over what interval is the graph of f(x)=-(x+8)^2-1 decreasing? (-8,infty ) (8,infty ) (-infty ,8) (-infty ,-8)

Solution
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Answer

(-8, \infty) Explanation 1. Identify the Vertex The function f(x) = -(x+8)^2 - 1 is a downward-opening parabola. The vertex form is f(x) = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = -8 and k = -1. 2. Determine Decreasing Interval For a downward-opening parabola, the graph decreases to the right of the vertex. Thus, it decreases for x > -8.

Explanation

1. Identify the Vertex<br /> The function $f(x) = -(x+8)^2 - 1$ is a downward-opening parabola. The vertex form is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex. Here, $h = -8$ and $k = -1$.<br />2. Determine Decreasing Interval<br /> For a downward-opening parabola, the graph decreases to the right of the vertex. Thus, it decreases for $x > -8$.
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