Question

What is the midpoint of the x-intercepts of f(x) = (x – 2)(x – 4)? (–3,0) (–1,0) (1,0) (3,0)

Answer 1

The correct option 4.

Explanation:

The given function is

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

At x-intercepts the value of f(x) is 0.

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

Using zero product property, equate each factor equal to 0.

`x-2=0`

`x=2`

`x-4=0`

`x=4`

The x-intercepts of the function are (2,0) and (4,0).

Midpoint of two points is

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

The midpoint of x-intercepts is

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

`M=(3,2)`

Therefore option 4 is correct.

Answer 2

the x intercepts are always on the x axis, those are the 'zeroes' or 'roots' of the function

f(x)=(x-r1)(x-r2)...(x-rn) where r1 to rn are roots or intercepts
f(x)=(x-2)(x-4)
the x intercepts are x=2 and x=4
xintercepts are (2,0) and (4,0)
what is between 2 and 4?
3
(3,0) is answer