what is the midpoint of the x - intercepts of f(x)=(x - 4)(x + 4)? (0,0) (0,4) (-4,0) (2,0)
what is the midpoint of the x - intercepts of f(x)=(x - 4)(x + 4)? (0,0) (0,4) (-4,0) (2,0)
Answer
Explanation:
Step1: Find x - intercepts
Set $f(x)=0$, so $(x - 4)(x + 4)=0$. Then $x-4 = 0$ or $x + 4=0$, which gives $x_1=4$ and $x_2=-4$.
Step2: Use mid - point formula
The mid - point formula for two points $x_1$ and $x_2$ on the x - axis (y - coordinate of x - intercepts is 0) is $(\frac{x_1 + x_2}{2},0)$. Substitute $x_1 = 4$ and $x_2=-4$ into the formula: $\frac{4+( - 4)}{2}=0$. So the mid - point is $(0,0)$.
Answer:
A. $(0,0)$