\[\frac{1}{4}y^{2} - y + 2 =\]
\[= \frac{1}{4}\left( y^{2} - 4y + 8 \right) =\]
\[= \frac{1}{4}\left( y^{2} - 4y + 4 + 4 \right) =\]
\[= \frac{1}{4}(y - 2)^{2} + 1\]