Consider the equation $y=(x+6)^2−7$.

1. Explain completely how to get a good sketch of the graph of $y=(x+6)^2−7$.

   Answer (a):

   Graph $y=x^2$ but shift the graph 6 units to the left and 7 units down.

2. Explain how to change the graph from part (a) to represent the graph of $y=(x+6)^2+2$.

   Answer (b):

   It would move up 9 units.

3. Given the original graph, how can you get the graph of $y=\left|(x+6)^2-7\right|$?

   Hint (c):

   Substitute $x=−5$ into the new, absolute value equation and into the original. How do the outputs differ?

   More Help (c):

   All the points that had negative y-values will now have positive y-values.

4. Restrict the domain of the original parabola to $x\ge−6$ and graph its inverse function.

   Hint (d):

   The inverse function is now an $x=y^2$ parabola with its vertex at $(−7,−6)$. For the inverse, $y\ge−6$. Why?

5. What would be the equation for the inverse function if you restricted the domain to $x\ge−6$?

   Hint (e):

   Interchange $x$ and $y$ in the original equation and solve for $y$.

   Use the eTool below to explore the graphs needed to solve the parts of the problem.
   Click the link to the right for full version. CCA2 5-80 HW eTool