Flying T-Shirts - Math Worksheet - Coordinate Geometry & Quadratic Functions

Oct 3, 2026

Instructional math worksheet about modeling a launched T-shirt’s flight at a varsity basketball game using the quadratic path y = −0.05x2 + 2.5x, with y as vertical height (feet) and x as horizontal distance (feet). Students place bleachers on a coordinate plane (starting 32 ft from center court) and determine the bleacher row hit by solving intersections of the quadratic path with a line. Additional tasks rewrite the equation into vertex form, verify equivalence, analyze coefficients and key points, and predict how the graph changes if the maximum height becomes 40 ft.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Flying T-Shirts

Problem Questions

Rubric and Point Breakdown

Name: Date: At a Varsity Basketball game, free T-shirts are being shot into the audience from a floor launcher. Chan wants to make sure his girlfriend catches the T-shirt, so they need to figure out which bleacher row she should sit in. Chan launches from center court. The Tshirt’s travel path, according to the manufacturer’s manual, is represented by the equation y = −0.05x2 + 2.5x, where y represents the vertical height in feet in terms of the horizontal distance traveled, x, in feet. The bleachers begin 32 feet from center court and each bleacher row has a height of 1.5 feet and a width of 2 feet as shown in the diagram. Use a line to represent the bleachers which touches the front edge of each row of seat and touches the floor 30 feet from center court as shown in the diagram. The diagram is not necessarily drawn to scale. Flying T-Shirts 2 ft 1.5 ft Center Court 30 Bleachers 1. If the center court is represented by the origin on a coordinate plane, what is the equation for the line that touches the front edge of each of the bleachers? 2. What row should Chan tell his girlfriend to sit in to get the T-shirt? Explain how you determined your answer. 3. An equivalent form ofthe T-shirt’s travel path y = −0 .05x2 + 2 .5x is y = −0 .05(x − 25)2 + 31 .25 . What form of the equation is the new form? Confirm they are equivalent. 4. What do you notice about the coefficient in the equation y = −0 .05(x − 25)2 + 31 .25 and key points about the T-shirts path? 5. How do you think the equation y = −0 .05(x − 25)2 + 31 .25 would change if the T-shirt reached a maximum height of 40 feet? Justify your reasoning. | Flying T-Shirts Rubric | | | | --- | --- | --- | | The core elements of performance required by this task are:
• Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Based on these, credit for specific aspects of performance should be assigned as follows. | points | section
points | | 1. Gives correct answer: 􀢟 = 􀫜􀫝 􀢞 − 􀫛􀫛 . 􀫞 | 1 | 1 | | 2. Gives correct answer: 8th row
Gives a correct explanation such as:
The point of intersection is (45,11.25), which means that the t-shirt has travelled 45 ft. horizontally when it strikes the line representing the bleachers at a height of 11.25 ft. This places the shirt in the 8th row by this logic:
This point would be 45-30=15 ft into the bleachers horizontally which would place in the 8th row. Each row is 2ft wide so 15 ft would be in the middle of the 8th row, which ends at 16 ft. | 1
1 | 2 | | 3. Gives correct answer: Vertex form
Shows work to prove the equations are equivalent | 1
1 | 2 | | 4. Gives correct answers such as:
• The coefficient ofthe x2 is the same.
• The number subtracted from x in the parenthesis is the horizontal location of the maximum.
• The number added at the end is the vertical maximum height. | 1
1
1 | 3 | | 5. Gives correct answer such as:
􀢟 = − . 􀫙􀫞 􀵫􀢞 – 􀫛􀫞􀵯 􀫛 + 􀫝􀫙
This makes the flight a little unrealistic, as the initial height would be 8.5 ft. | 1 | 1 | | Total Points | | 9 |

FAQs

How do you find the bleacher row where the T-shirt lands?

Set the T-shirt path equation equal to the bleachers line that represents the front edge and floor touch. The intersection point gives the x-distance traveled; convert to how far into the bleachers and determine the row width.

What is the vertex form of the T-shirt travel path, and how is it confirmed?

Rewrite y = −0.05x2 + 2.5x as y = −0.05(x − 25)2 + 31.25. Confirm equivalence by expanding the vertex form and matching coefficients with the original equation.

What does the coefficient in y = −0.05(x − 25)2 + 31.25 tell you about the T-shirt’s path?

The coefficient of x2 (here, −0.05) stays the same as in the original quadratic, indicating the parabola opens downward. The value subtracted inside (25) marks the horizontal location of the maximum, and the added constant (31.25) is the vertical maximum height.

Oct 3, 2026

Uploaded by Genevieve