Question

What is the midpoint of the x-intercepts of f(x) = (x – 4)(x + 4)?

Answer 1

f(x) = (x – 4)(x + 4) = x^2 - 4.  This is the equation of a parabola with vertex at (0,-4) and x-intercepts of (-2,0) and (2,0).  The midpoint of the line segment connecting these 2 points is (0,0).  Draw this situation and see for yourself!

Answer 2

Answer:  The correct option is (A) (0, 0).

Step-by-step explanation:  We are given to find the midpoint of the x-intercepts of the following quadratic function:

$f(x)=(x-4)(x+4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that the x-intercepts of a function f(x) is found by solving the equation f(x) = 0.

So, from equation (i), we have

$f(x)=0\\\\\Rightarrow (x-4)(x+4)=0\\\\\Rightarrow x-4=0,~~~~~x+4=0\\\\\Rightarrow x=4,~-4.$

That is, the x-intercepts of the given function are the points (4, 0) and (-4, 0).

Therefore, the co-ordinates of the mid-point of the x-intercepts (4, 0) and (-4, 0) will be

$\left(\dfrac{4+(-4)}{2},\dfrac{0+0}{2}\right)\\\\\\=(0,0).$

Thus, the required mid-point of the x-intercepts is (0, 0).

Option (A) is correct.