### Home > A2C > Chapter 11 > Lesson 11.3.1 > Problem11-134

11-134.

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?

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

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

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

See part (a).

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

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

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

4. When will the rocket hit the ground?

See the graph from part (b).

5. What is the domain for this function?

See the graph from part (b).

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

See the graph from part (b).