IM Alg1.6.6 Lesson: Building Quadratic Functions to Describe Situations (Part 2)
A cannon is 10 feet off the ground. It launches a cannonball straight up with a velocity of 406 feet per second.
Complete the table with the heights of the cannonball at different times.
Write an equation to model the distance in feet, , of the ball seconds after it was fired from the cannon if there was no gravity.
Earlier, you completed a table that represents the height of a cannonball, in feet, as a function of time, in seconds, if there was no gravity.
This table shows the actual heights of the ball at different times.
Plot the two sets of data you have on the same coordinate plane. Right click on a point to find the setting to change its color.
How are the two graphs alike? How are they different?
Write an equation to model the actual distance , in feet, of the ball seconds after it was fired from the cannon. If you get stuck, consider the differences in distances and the effects of gravity from a previous lesson.
The function defined by gives the height in feet of a cannonball seconds after the ball leaves the cannon. What do the terms 50, , and tell us about the cannonball?
Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: 0 < x < 25 and 0 < y < 2,000.
Observe the graph and:
Describe the shape of the graph. What does it tell us about the movement of the cannonball?
Estimate the maximum height the ball reaches. When does this happen?
Estimate when the ball hits the ground.
What domain is appropriate for this function? Explain your reasoning.
If the cannonball were fired at 800 feet per second, would it reach a mile in height? Explain your reasoning.