Answer
The vertex is $\left( 2,-1 \right)$ and axis of symmetry is $y=-1$.
Work Step by Step
$\begin{align}
& x={{y}^{2}}+2y+1+2 \\
& ={{y}^{2}}+y+y+1+2 \\
& =y\left( y+1 \right)+1\left( y+1 \right)+2 \\
& =\left( y+1 \right)\left( y+1 \right)+2
\end{align}$
Further simplify,
$x={{\left( y+1 \right)}^{2}}+2$
Compare it with the standard equation of a parabola,
$a=1,h=2$ and $k=-1$
