### Home > INT3 > Chapter 12 > Lesson 12.1.1 > Problem 12-18

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 8 seconds. Homework Help ✎ What are three data points that can represent this situation?

Sketch a graph of the height of the rocket over time.

Model the data with a quadratic function.

When will the rocket hit the ground?

What is an appropriate domain for this situation?

When is the rocket below ground?

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

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

Substitute each point into the equation *y* = *ax*^{2} + *bx* + *c*.

You will have a system of three equations with three unknowns.

Using your equation from part (c), let *y* = 0 and solve for *x*.

Note: You should get two answers. Which one is it?

Look at your graph and the answer to part (d). 0 ≤ *x* ≤ ?

Look at your graph and the answer in part (d) that you did not use. 0 ≤ *x* ≤ ?