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

Question

Quizplus · Accepted Answer

The graph is shifted 3 units to the left, so $x$ becomes $x + 3$. It is vertically compressed by $\frac{1}{5}$ and reflected across the $x$-axis, so the equation becomes $-\frac{1}{5}(x + 3)^2$. Finally, it is shifted 7 units downward, resulting in $-\frac{1}{5}(x + 3)^2 - 7$.

Write the Equation of the Graph After the Indicated Transformation(s) y=x2y = x ^ { 2 }y=x2

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