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A small rocket is launched from five meters below ground level and reaches a height of meters above the ground after seconds. On the way down it is meters above the ground after a total of seconds.

  1. What are three data points?

    Each point is (time, height). The first one is .

  2. Draw a rough sketch of the height of the rocket over time.

    Plot the three points you listed in part (a). Then sketch a parabola through them.

  3. Find the equation of the parabola based on the data.

    See the hints and help for problem 10-154.

  4. When will the rocket hit the ground?

    Using your equation from part (c), let (or ) and solve for (or ).
    Note: You should get two answers. Which one is it?

  5. What is the domain for this function?

    Look at your graph and the answer to part (d). ?

  6. For what part of the domain is the rocket below ground?

    Look at your graph and the answer in part (d) that you did not use. ?