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10-163.

A small rocket is launched from five meters below ground level and reaches a height of $3$ meters above the ground after $4$ seconds. On the way down it is $3$ meters above the ground after a total of $8$ seconds.

1. What are three data points?

Each point is (time, height). The first one is $(0, -5)$.

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 $h$ (or $y$) $= 0$ and solve for $t$ (or $x$).
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). $0 ≤ t ≤$ ?

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. $0 ≤ t ≤$ ?