consider the graph of the function $f(x)=2(x + 3)^2+2$. over which interval is the graph decreasing?\n$(-\\in…

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

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

Answer

Explanation:

Step1: Identify the function type

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

Step2: Analyze the sign of $a$

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

Step3: Determine the vertex

The vertex of the parabola is at the point $(h,k)=(-3,2)$.

Step4: Find the decreasing interval

For a parabola that opens upward, the function is decreasing to the left of the vertex. So the decreasing interval is $(-\infty,-3)$.

Answer:

$(-\infty,-3)$