Answer
$y=-(x+1)^2+5$
Work Step by Step
\begin{align*}
&y=(-x^2-2x)+3 &\text{Group the terms with variables together.}\\
&y=-1(x^2+2x)+3 &\text{Factor out $-1$.}\\
&y=-(x^2+2x)+3 \\
\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+2x+\color{blue}{\left(\frac{2}{2}\right)^2}\right]+3-\color{red}{-\left(\frac{2}{2}\right)^2} &\text{Complete the square.}\\\\
&y=-\left[x^2+2x+1\right]+3-(-1) &\text{Simplify.}\\\\
&y=-(x+1)^2+1+4\\\\
&y=-(x+1)^2+5
\end{align*}
