Answer
part $\left( c \right)$
Work Step by Step
The standard form of the equation of the parabola vertex of the parabola at $\left( h,k \right)$ is defined as,
$y=a{{\left( x-h \right)}^{2}}+k$
Compare the provided equation with the standard form of the equation of the circle. It shows that the provided equation is the equation of a circle.
The values of $h\text{ and }k$ are obtained as:
$\begin{align}
& x-h=x-2 \\
& -h=-2 \\
& h=2
\end{align}$
And,
$k=-5$
So, the vertex of the parabola is obtained as $\left( 2,-5 \right)$.
The correct match for the graph of the equation $y={{\left( x-2 \right)}^{2}}-5$ is graph (c).
