Answer
Option (d)
Work Step by Step
The provided function,
$x={{\left( y-2 \right)}^{2}}-5$
On comparing the above equation with $x={{\left( y-k \right)}^{2}}+h$ where $\left( h,k \right)$ is vertex, the vertex will be $\left( -5,2 \right)$. To find ordered pairs, choose values for $y$ on each side of the vertex.
Then compute the values of $x$ and $y$ with the help of the given equation in below table.
$\begin{matrix}
x & y \\
-5 & 2 \\
-1 & 0 \\
4 & 5 \\
4 & -1 \\
11 & 6 \\
\end{matrix}$
From the graph it can be found that this is the graph of parabola which has the vertex $\left( -5,2 \right)$.
The graph that matches with the provided equation is the graph of option (d).
