Question

What is the midpoint of the x-intercepts of f(x) = (x – 2)(x – 4)?

A)(–3,0)
B)(–1,0)
C)(1,0)
D)(3,0)

Answer 1

The x-intercepts are readily identified on the graph:  (2,0) and (4,0).  The midpoint of a line connecting those 2 points would be (3,0).

Answer 2

The correct option is D.

Explanation:

The given function is

`f(x)=(x-2)(x-4)`

From the given graph it is clear that x-intercepts of the graph are (2,0) and (4,0).

The midpoint of x-intercepts is

`Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))`

`Midpoint=((2+4)/(2),(0+0)/(2))`

`Midpoint=((6)/(2),(0)/(2))`

`Midpoint=(3,0)`

The midpoint of x-intercepts is (3,0). Therefore the correct option is D.