Answer:
The midpoint of the x-intercepts of f(x) is (3,0).
Step-by-step explanation:
The given function is
\(f(x)=(x-2)(x-4)\)
To find the x-intercepts equation f(x) equals to 0.
\(f(x)=0\)
\((x-2)(x-4)=0\)
Using zero product property, equate each factor equals to 0.
\(x-2=0\Rightarrow x=2\)
\(x-4=0\Rightarrow x=4\)
The x-intercepts are (2,0) and (4,0). The midpoint of x-intercepts of f(x) is
\(Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)
\(Midpoint=(\frac{2+4}{2},\frac{0+0}{2})\)
\(Midpoint=(3,0)\)
Therefore midpoint of the x-intercepts of f(x) is (3,0).
