\[2y^{2} - 4y - 1 =\]
\[= 2 \cdot \left( y^{2} - 2y - \frac{1}{2} \right) =\]
\[= 2 \cdot \left( y^{2} - 2y + 1 - \frac{3}{2} \right) =\]
\[= 2 \cdot \left( (y - 1)^{2} - \frac{3}{2} \right) =\]
\[= 2 \cdot (y - 1)^{2} - 3\]