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

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

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

  3. Given the original graph, how can you get the graph of ?

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

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

Graph y = x2 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 = y² 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.
Click the link to the right for full version. CCA2 5-80 HW eTool