Answer
$f(x)= -2(x-5)^2+6$
Work Step by Step
Given \begin{equation}
f(x)=-2 x^2+20 x-44.
\end{equation} Complete the square: \begin{equation}
\begin{aligned}
f(x)&=-2 x^2+20 x-44\\
&= -2\left(x^2-10x+22\right)\\
& =-2\left[x^2-10x+5^2+22-5^2\right]\\
& =-2\left[(x-5)^2-3\right]\\
& = -2(x-5)^2+6.
\end{aligned}
\end{equation} The function in vertex is given as: \begin{equation}
f(x)= -2(x-5)^2+6.
\end{equation}
