Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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).