Answer
$y=2(x-2)^2-7$
Work Step by Step
\begin{align*}
&y=(2x^2-8x)+1 &\text{Group the terms with variables together.}\\
&y=2(x^2-4x)+1 &\text{Factor out $2$.}\\
\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=2\left[x^2-4x+\color{blue}{\left(\frac{-4}{2}\right)^2}\right]+1-\color{red}{2\left(\frac{-4}{2}\right)^2} &\text{Complete the square.}\\\\
&y=2\left[x^2-4x+4\right]+1-2(4) &\text{Simplify.}\\\\
&y=2(x-2)^2+1-8\\\\
&y=2(x-2)^2-7
\end{align*}
