Question

for the following exercise, determine the interval(s) on which the function in increasing and decreasing. enter \dne\ if the function is never increasing or decreasing.
$f(x)=2(x + 9)^2 - 3$
increasing:
decreasing:

Explanation:

Step1: Identify parabola vertex & direction

The function $f(x)=2(x+9)^2-3$ is a parabola in vertex form $a(x-h)^2+k$, with vertex at $(-9, -3)$ and $a=2>0$, so it opens upward.

Step2: Find increasing interval

For upward-opening parabolas, the function increases to the right of the vertex.
Interval: $(-9, \infty)$

Step3: Find decreasing interval

For upward-opening parabolas, the function decreases to the left of the vertex.
Interval: $(-\infty, -9)$

Answer:

Increasing: $(-9, \infty)$
Decreasing: $(-\infty, -9)$