Egg Launch Task_Quadratics
Egg Launch Contest
Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using models of quadratic functions. Use knowledge of transformations to write an equation, given the graph of a quadratic function.
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Which team won the egg launching contest?
Mr. Rhodes’ class is holding an egg launching contest on the football field. Teams of students have built catapults that will hurl an egg down the field. Ms. Monroe’s class will judge the contest. They have various tools and ideas for measuring each launch and how to determine which team wins. Team A used their catapult and hurled an egg down the football field. Students used a motion detector to collect data while the egg was in the air. They came up with the table of data below.
Team A
| DISTANCE FROM THE GOAL LINE(IN FEET) | HEIGHT(IN FEET) |
| 7 | 19 |
| 12 | 90 |
| 14 | 101 |
| 19 | 90 |
| 21 | 55 |
| 24 | 0 |
Team B’s egg flew through the air and landed down the field. The group of students tracking the path of the egg determined that the equation y = –0.8x2+ 19x – 40 represents the path the egg took through the air, where x is the distance from the goal line and y is the height of the egg from the ground. (Both measures are in feet.)
When Team C launched an egg with their catapult, some of the judges found that the graph to the right shows the path of the egg.
Which team do you think won the contest? Why?
Team A
1. Using the data from Team A, determine an equation that describes the path of the egg. Describe how you found your equation.
2. On the graph below, graph the path of Team A’s egg.
3. What is the maximum height that the egg reached? How far was the egg hurled?
Team B
4. Using the equation from Team B, generate a table of values that shows different locations of the egg as it flew through the air.
| x | |||||||||||
| y |
5. On the graph below, graph the path of Team B’s egg.
6. What is the maximum height that the egg reached? How far was the egg hurled?
Team C
7. Using the data from Team C, generate a table of values that shows different locations of the egg as it flew through the air.
| x | |||||||||||
| y |
8. On the graph below, re-graph the path of Team C’s egg.
9. What is the maximum height that the egg reached? How far was the egg hurled?
10. If it is a height contest, which team wins? How do you know?
11. If it is a distance contest, which team wins? Explain how you know.
12. Find a method of determining a winner so that the team that did not win in Question 10 or Question 11 would win using your method.
