select the correct answer from each drop - down menu. what is the end behavior of function h? h(x)=2(x…

Explanation:

Step1: Analyze the function form

The function $h(x)=2(x - 3)^2$ is a quadratic function in vertex - form $y=a(x - h)^2+k$, where $a = 2$, $h=3$ and $k = 0$. Since $a=2>0$, the parabola opens upward.

Step2: Consider $x\to-\infty$

As $x\to-\infty$, we have $(x - 3)^2\to\infty$. Multiply by $a = 2$ (a positive constant), so $h(x)=2(x - 3)^2\to\infty$.

Step3: Consider $x\to+\infty$

As $x\to+\infty$, $(x - 3)^2\to\infty$. Multiply by $a = 2$ (a positive constant), so $h(x)=2(x - 3)^2\to\infty$.

Answer:

As $x$ approaches negative infinity, $h(x)$ approaches $\infty$. As $x$ approaches positive infinity, $h(x)$ approaches $\infty$.