Write the Equation of the Graph After the Indicated Transformation(s) $y = x ^ { 2 }$

Multiple Choice

Write the equation of the graph after the indicated transformation(s) .
-The graph of $y = x ^ { 2 }$ is shifted 3 units to the left. This graph is then vertically compressed by a factor of $\frac { 1 } { 5 }$ and reflected across the $x$ -axis. Finally, the graph is shifted 7 units downward.

A) $y = \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$
B) $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$
C) $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 7$
D) $y = - \frac { 1 } { 5 } ( x + 3 ) ^ { 2 } - 7$