the graph of which function is decreasing over the interval (-4, ∞)?\no f(x)=(x + 4)^2+4\no f(x)=-(x +…

Explanation:

Step1: Recall vertex - form of 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 if (a < 0), the parabola opens downward. The function is increasing on one side of the vertex and decreasing on the other side.

Step2: Analyze each option

Option 1: (f(x)=(x + 4)^2+4)

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

Option 2: (f(x)=-(x + 4)^2+4)

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

Option 3: (f(x)=(x - 4)^2-4)

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

Option 4: (f(x)=-(x - 4)^2-4)

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

Answer:

(f(x)=-(x + 4)^2+4)