what is the midpoint of the x - intercepts of f(x)=(x - 4)(x + 4)?\n(0,0)\n(0,4)\n(-4,0)\n(2,0)

Explanation:

Step1: Find x - intercepts

Set $f(x)=(x - 4)(x + 4)=0$. Then $x-4 = 0$ or $x + 4=0$. Solving these equations gives $x=4$ and $x=-4$.

Step2: Calculate mid - point

The mid - point formula for two points $x_1$ and $x_2$ on the x - axis is $x=\frac{x_1 + x_2}{2}$. Here $x_1=-4$ and $x_2 = 4$. So $x=\frac{-4 + 4}{2}=0$. Since we are finding the mid - point of x - intercepts, the y - coordinate is 0. The mid - point is $(0,0)$.

Answer:

A. $(0,0)$