the graph of which function is decreasing over the interval (-4, ∞)?\n○ (f(x)=(x + 4)^2+4)\n○ (f(x)=-(x +…

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $y = a(x - h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. If $a>0$, the parabola opens upward and is decreasing on the interval $(-\infty,h)$ and increasing on the interval $(h,\infty)$. If $a < 0$, the parabola opens downward and is increasing on the interval $(-\infty,h)$ and decreasing on the interval $(h,\infty)$.

Step2: Analyze each function

For $f(x)=(x + 4)^{2}+4$

Here, $a = 1>0$, $h=-4$, $k = 4$. The parabola opens upward and is decreasing on the interval $(-\infty,-4)$ and increasing on the interval $(-4,\infty)$.

For $f(x)=-(x + 4)^{2}+4$

Here, $a=-1<0$, $h = - 4$, $k = 4$. The parabola opens downward and is increasing on the interval $(-\infty,-4)$ and decreasing on the interval $(-4,\infty)$.

For $f(x)=(x - 4)^{2}-4$

Here, $a = 1>0$, $h = 4$, $k=-4$. The parabola opens upward and is decreasing on the interval $(-\infty,4)$ and increasing on the interval $(4,\infty)$.

For $f(x)=-(x - 4)^{2}-4$

Here, $a=-1<0$, $h = 4$, $k=-4$. The parabola opens downward and is increasing on the interval $(-\infty,4)$ and decreasing on the interval $(4,\infty)$.

Answer:

$f(x)=-(x + 4)^{2}+4$