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 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

Answer 2

Answer:

The correct option 4.

Step-by-step 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

$M=(\frac{x_1+x_2}{2},\frac{y_1-y_2}{2})$

The midpoint of x-intercepts is

$M=(\frac{2+4}{2},\frac{0+0}{2})$

$M=(3,2)$

Therefore option 4 is correct.