Answer
Option (a)
Work Step by Step
The provided function,
$x={{\left( y-5 \right)}^{2}}-2$
On comparing the above equation with $x={{\left( y-k \right)}^{2}}+h$ where $\left( h,k \right)$ is vertex, the vertex will be $\left( -2,5 \right)$. 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.
$\begin{matrix}
x & y \\
-2 & 5 \\
2 & 7 \\
2 & 3 \\
7 & 8 \\
7 & 2 \\
\end{matrix}$
From the graph it can be found that this is the graph of a parabola which has the vertex $\left( -2,5 \right)$.
Thus, (a).
