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5-80.

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 $y = | ( x + 6 ) ^ { 2 } - 7$?

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.
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