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Consider the equation .

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

    Graph 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 .

    It would move up 9 units.

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

    Substitute 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.

  4. Restrict the domain of the original parabola to and graph its inverse function.

    The inverse function is now an parabola with its vertex at . For the inverse, . Why?

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

    Interchange and in the original equation and solve for .

    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