Answer
$\left( \dfrac{9}{2},-\dfrac{49}{4} \right)$
Work Step by Step
The standard form of the given quadratic function, $f(x)=
x^2-9x+8
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( x^2-9x \right)+8
\\\\
f(x)=\left( x^2-9x+\left( \dfrac{9}{2} \right)^2 \right)+8-\left( \dfrac{9}{2} \right)^2
\\\\
f(x)=\left( x^2-9x+\dfrac{81}{4} \right)+8-\dfrac{81}{4}
\\\\
f(x)=\left( x-\dfrac{9}{2} \right)^2+\dfrac{32}{4}-\dfrac{81}{4}
\\\\
f(x)=\left( x-\dfrac{9}{2} \right)^2-\dfrac{49}{4}
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is
\begin{array}{l}\require{cancel}
\left( \dfrac{9}{2},-\dfrac{49}{4} \right)
.\end{array}
