the graph of the function f(x)=-(x + 6)(x + 2) is shown below. which statement about the function is true…

the graph of the function f(x)=-(x + 6)(x + 2) is shown below. which statement about the function is true? the function is increasing for all real values of x where x < -4. the function is increasing for all real values of x where -6 < x < -2. the function is decreasing for all real values of x where x < -6 and where x > -2. the function is decreasing for all real values of x where x < -4.

the graph of the function f(x)=-(x + 6)(x + 2) is shown below. which statement about the function is true? the function is increasing for all real values of x where x < -4. the function is increasing for all real values of x where -6 < x < -2. the function is decreasing for all real values of x where x < -6 and where x > -2. the function is decreasing for all real values of x where x < -4.

Answer

Explanation:

Step1: Find the vertex of the parabola

First, expand the function $f(x)=-(x + 6)(x + 2)=-(x^{2}+8x + 12)=-x^{2}-8x - 12$. The $x$-coordinate of the vertex of a parabola $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. Here $a=-1$ and $b = - 8$, so $x=-\frac{-8}{2\times(-1)}=-4$.

Step2: Analyze the opening - direction of the parabola

Since $a=-1<0$, the parabola opens downwards. A parabola that opens downwards is increasing to the left of the vertex and decreasing to the right of the vertex.

Answer:

The function is increasing for all real values of $x$ where $x < - 4$.