Verified Answer :

apologiabiology

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:

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.

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