Eric is participating in a pumpkin-launching competition using a homemade air cannon. He collected three points of data from his launch, but wants to determine some specifics about the launch from the data. The table contains the data he collected. Time from Launch, t (seconds) Height of Pumpkin, h (feet)
0 0
2 272
10.5 0
Use this data to complete the task.
Part A
The motion of a projectile, comparing height over time, can be modeled using a quadratic function. To model this situation with a quadratic function, first identify two of the factors of the quadratic by identifying the zeros in the data points.

Part B
Now that you have two factors, you need to determine what constant to multiply them by to find the actual function. To do this, let c represent the unknown constant, t represent time, and h represent height. Then, use the middle data point to find the value of c and write a function to model the situation. Show your work.

Part C
All projectile motion situations can be modeled by the function , where a represents the vertical acceleration acting on the projectile (this is generally the acceleration due to gravity), represents the initial vertical velocity of the projectile, and represents the initial height of the object.

Using this information, what is the initial vertical velocity of the pumpkin when it is launched?

Part D
The maximum height of the pumpkin will occur exactly halfway between the zeros of the function. Determine the maximum height Eric’s pumpkin will reach during its flight. Show your work.