Quadratics All Around

Once you start looking for them, the world is filled with parabolas. This month, students in Louise Lu’s Extended Topics in Algebra and Geometry class presented their “Quadratics All Around Us” projects, where they identified a parabola in the real world and analyzed it as a quadratic function. Each student graphed their parabola in Desmos, wrote the corresponding quadratic equation in vertex and standard form, identified key features of their quadratic, and created a vertical velocity word problem connected with their image. Once the projects were complete, students presented their work to the class.

Extended Topics in Algebra and Geometry is a class for Upper School students who have been exposed to algebra and geometry and are strong enough math students to take the equivalent of Algebra 1 and Geometry in a single year. The first half of the year is spent on Algebra and the second half on geometry. The class focuses on problem-solving in context and consequently incorporates various projects that highlight the real-world applications of math skills. 

The quadratic function is critical in algebra and is graphed in a curve called a parabola, which can face up or down. Students identified a parabola to study and, in most cases, heeded Louise’s suggestion to pick something fun. They chose real-world parabolas, including the arch of a cat’s back, Pikachu’s outline, and even the chin of a classmate! After graphing each image in Desmos, students had to correctly write the quadratic equation and identify points in the parabola, including the vertex, the x and y intercepts, the axis of symmetry, and the roots. As students presented their projects to the class, they explained and answered questions about how they came up with the points in their graph. “We see the data, but behind that is a lot of calculation, so talking about those different data points is how I see their understanding,” says Louise. 

Connecting quadratics with real-world objects helps students understand how math applies to their lives. Louise points out the utility of the quadratic formula in designing buildings, bridges, and arches to make the most perfect and stable shape possible. She hopes that projects like this help her students appreciate math’s functionality. “Math is not just in the classroom,” says Louise, “If you look around and observe, math is everywhere.”