Answer
Parabola.
Work Step by Step
$x={{\left( y+3 \right)}^{2}}+2$
It is written as:
$\begin{align}
& x={{\left( y+3 \right)}^{2}}+2 \\
& {{\left( y+3 \right)}^{2}}=x-2 \\
& {{\left( y+3 \right)}^{2}}=4\left( \frac{1}{4} \right)\left( x-2 \right)
\end{align}$
The above equation is a standard form of a parabola ${{\left( y-k \right)}^{2}}=4a(x-h)$.
Therefore, it is a parabola equation.
Graph:
The vertices of the parabola are $\left( h,k \right)=\left( 2,-3 \right)$, and the focus of the parabola is $\left( a,0 \right)=\left( \frac{1}{4},0 \right)$.
Therefore, the graph of the parabola $x={{\left( y+3 \right)}^{2}}+2$ is shown below:
