### Home > CCA2 > Chapter 5 > Lesson 5.2.2 > Problem 5-80

Consider the equation *y* = (*x* + 6)^{2} − 7. *5-80 HW eTool* (Desmos). Homework Help ✎

Explain completely how to get a good sketch of the graph of

*y*= (*x*+ 6)^{2}− 7.Explain how to change the graph from part (a) to represent the graph of

*y*= (*x*+ 6)^{2}+ 2.Given the original graph, how can you get the graph of

? Restrict the domain of the original parabola to

*x*≥ −6 and graph its inverse function.What would be the equation for the inverse function if you restricted the domain to

*x*≥ −6?

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

It would move up 9 units.

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

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

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

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.

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