Write the equation of the graph after the indicated transformation(s).
-The graph of $y = x ^ { 2 }$ is shifted 2 units to the left. This graph is then vertically stretched by a factor of 6 and reflected across the $x$-axis. Finally, the graph is shifted 8 units downward.
A) $y = - 6 ( x + 8 ) ^ { 2 } - 2$
B) $y = - 6 ( x + 2 ) ^ { 2 } - 8$
C) $y = - 6 ( x - 2 ) ^ { 2 } + 8$
D) $y = - 6 ( x - 2 ) ^ { 2 } - 8$

Question

Quizplus · Accepted Answer

The correct transformations in order are: shift 2 units left (replace $x$ with $x + 2$), vertical stretch by a factor of 6 (multiply the function by 6), reflection across the $x$-axis (multiply the function by -1), and shift 8 units downward (subtract 8 from the function). This results in $y = -6(x + 2)^2 - 8$.

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) $y = x ^ { 2 }$