Answer
$(1/2, 5/4)$
Work Step by Step
$f(x)=-x^2+x+1$
$f(x)=-(x^2-x)+1$
$f(x)=-(x^2-x+(-1/2)^2)+1+(-1/2)^2$
$f(x)=-(x^2-x+1/4)+1+1/4$
$f(x)=-(x-1/2)^2+5/4$
The vertex is of the form $(h,k)$, and this quadratic equation is of the form $f(x)=a(x−h)^2+k$.
$(1/2, 5/4)$ is the vertex.