Answer
$y=-\left(x-2\right)^2+3$
Work Step by Step
\begin{align*}
&y=(-x^2+4x)-1 &\text{Group the terms with variables together.}\\
&y=-1(x^2-4x)-1 &\text{Factor out $-1$.}\\
&y=-(x^2-4x)-1 \\
\end{align*}
Recall:
To complete the square of $y=a(x^2+bx)+c$, you add $\left(\dfrac{b}{2}\right)^2$ inside the parentheses and subtract $a\cdot \left(\dfrac{b}{2}\right)^2$ outside to obtain $y=a\left[x^2+bx +\color{blue}{\left(\dfrac{b}{2}\right)^2}\right]+c-\color{red}{a\left(\dfrac{b}{2}\right)^2}$
\begin{align*}
&y=-\left[x^2-4x+\color{blue}{\left(\frac{-4}{2}\right)^2}\right]-1-\color{red}{-\left(\frac{-4}{2}\right)^2} &\text{Complete the square.}\\\\
&y=-\left[x^2-4x+4\right]-1+4 &\text{Simplify.}\\\\
&y=-\left(x-2\right)^2+3\\\\
\end{align*}
