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

1. What are three data points?

   Hint (a):

   Define the variables;$x = \text{time}, y = \text{height}$.

   Answer (a):

   $\left(0, −5\right), \left(4, 3\right), \left(8, 3\right)$

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

   Hint (b):

   See part (a).

   Answer (b):

   

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

   Hint (c):

   Use the points from (a) and the general equation $y = ax^{2} + bx +$c.

   Answer (c):

   $y=-\frac{1}{4}x^{2}+3x-5$

4. When will the rocket hit the ground?

   Hint (d):

   See the graph from part (b).

5. What is the domain for this function?

   Hint (e):

   See the graph from part (b).

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

   Hint (f):

   See the graph from part (b).