Consider the equation $y = \left(x + 6\right)^{2} − 7$. .

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

   Answer (a):

   Graph a regular $y = x^{2}$, but place its vertex at (−6, −7).

2. Explain how to change the original graph to represent the graph of $y = \left(x + 6\right)^{2} + 2$.

   Answer (b):

   It would move vertically upwards.

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

   Hint (c):

   Remember the meaning of absolute value.

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

   Hint (d):

   Remember how to find the inverse of a function.

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