the graph of the function f(x)=(x + 2)(x - 4) is shown. which describes all of the values for which the…

Explanation:

Step1: Expand the function

$f(x)=(x + 2)(x - 4)=x^{2}-4x+2x - 8=x^{2}-2x - 8$.

Step2: Find the vertex of the parabola

The $x$-coordinate of the vertex of a parabola $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. For $y=x^{2}-2x - 8$, $a = 1$, $b=-2$. So $x=-\frac{-2}{2\times1}=1$.

Step3: Determine when the function is negative

Set $f(x)=x^{2}-2x - 8<0$. Factoring gives $(x + 2)(x - 4)<0$. The solution of the inequality is $-2<x<4$.

Step4: Determine when the function is increasing

Since $a = 1>0$, the parabola opens upward. The function is increasing for $x\geq1$.

Step5: Find the intersection

The intersection of $-2<x<4$ and $x\geq1$ is $1<x<4$.

Answer:

all real values of $x$ where $1 < x < 4$