Shahbaj needed to find the vertex for $y = −2x^{2} + 4x − 5$. He came up with $V\left(−1, 3\right)$. He checked his result by graphing the original equation on his graphing calculator. He found the vertex had the coordinates of $\left(1, −3\right)$. Shahbaj’s work is shown below. What was his error?

$\left. \begin{array} { l } { y + 5 = - 2 x ^ { 2 } + 4 x } \\ { y + 5 = - 2 ( x ^ { 2 } + 2 x ) } \\ { y + 5 + ( - 2 ) = - 2 ( x ^ { 2 } +2x + 1) } \\ { y + 3 = - 2 ( x + 1 ) ^ { 2 } } \\ { y = - 2 ( x + 1 ) ^ { 2 } - 3 } \end{array} \right.$