About 400 yr ago, the physicist Galileo observed that certain projectiles follow a parabolic path ...

where h is the elevation of the shell trajectory and d is the corresponding horizontal distance from the cannon when the elevation is h.

1. Does the graph of this equation open up or down? How did you determine this?

2. Describe what happens to the projectile as time passes.

3. Use the quadratic equation to determine at what distance from the cannon the shell hits the ground.

4. Will the shell be at a high point or be at a low point at the middle of the trajectory? How do you know?

5. What is the highest elevation the shell will attain?

6. When the shell is at its highest, how far (horizontally) will it be from the cannon?

7. What is the point of the vertex? How does this number relate to your answers in parts e. and f?

8.