Question

determining characteristics of a graph consider the graph of the function $f(x) = 2(x + 3)^2 + 2$. over which interval is the graph decreasing? $(-infty, -3)$ $(-infty, 2)$ $(-3, infty)$ $(2, infty)$

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x)=a(x-h)^2+k$, where $a=2$, $h=-3$, $k=2$.

Step2: Determine parabola direction

Since $a=2>0$, parabola opens upward.

Step3: Find decreasing interval

For upward parabola, it decreases left of vertex $x=h=-3$. Interval: $(-\infty, -3)$

Answer:

$(-\infty, -3)$