 # Nothing but Net…and Quadratic Equations

High school students recently covered multiple strategies to solve and graph mathematical functions for quadratic equations. This year the high school math department explored a new way of helping high school students see the relevance of higher level mathematical concepts in the physical world by introducing a real-world aspect of quadratic equations. High school mathematics teacher, Tricia Apel, details the students’ learning process. The Algebra II/ Trigonometry class explored the trajectory of a basketball by looking at free throw basketball shots. Students created videos of the different types of shots that could be made from the free throw line (short, long, swish, making it from the backboard). They then created videos of the different shots , allowing them to analyze the mathematical equations that result from various throws. Next, they put the videos into LoggerPro, a program that allows student to analyze movement, and mapped data points related to the ball’s trajectory through the air and its location at various points along that trajectory .

After logging those data points, students transferred that information into a powerful, HTML5-based graphing calculator program called Desmos. Students scaled the video so that it aligns with a graph in Desmos, then wrote the equation for the path of the ball. The students explored writing equations in vertex, factored and standard form for their analysis.

Once the students gained an understanding of the different equations for the various types of possible shots, they used that information to answer a question: “Will a basketball shot from the free throw line make it through the basket or not?”

Students must understand the various elements of a quadratic equation in order to make a mathematical prediction regarding the success of a free throw shot. They must also explore the real-life variables that could affect their mathematical conclusions.

This experience allowed students to explore a difficult mathematical concept that, without a real-world application, may seem very abstract. Mapping the trajectory of physical objects made the mathematics more concrete and applicable to their lives and learning.

We began learning about quadratic equations before winter break and are continuing to apply the concepts to complex fractions and irrational equations. What is great about quadratic equations is how easily the concept transfers into a range of diverse problems.