Answer
$m,n$
$(m+n)/2$
Work Step by Step
Clearly the x-intercepts are given by the x values when $f(x)=0$ which
means $x=m,n$. Based on the symmetry of the parabola curve, the
vertex happens at the middle points of the two x-intercepts, which
give $x_v=\frac{m+n}{2}$. We can confirm this by expanding the function
$f(x)=(x-m)(x-n)=x^2-mx-nx+mn=x^2-(m+n)x+mn$,
and this expression indicates that the vertex happens at $x=(m+n)/2$