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)
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)
Answer
Explanation:
Step1: Find x - intercepts
Set $f(x)=0$, so $(x - 4)(x + 4)=0$. Then $x-4 = 0$ gives $x = 4$ and $x + 4=0$ gives $x=-4$. The x - intercepts are $(4,0)$ and $(-4,0)$.
Step2: Use mid - point formula
The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-4,y_1 = 0,x_2 = 4,y_2=0$. So the mid - point is $(\frac{-4 + 4}{2},\frac{0+0}{2})=(0,0)$.
Answer:
A. $(0,0)$