An independent, college-preparatory day school serving grades 7 through 12.
The Ups and Downs of Quadratic Equations
Before the break, Mr. Nestor’s Algebra II students worked with quadratic equations to form parabolas. A parabola is a U-shaped plane where any point is at an equal distance from a fixed focal point and a fixed straight line.
For fun, the students designated each parabola example as either a smile or a frown depending on whether they arced up or down, respectively. Examples of parabolas are found in real life such as the cables used for suspension on the Golden Gate bridge, the rotating waters of a whirlpool, and even possibly the curve of a banana. The students practiced comparing various quantities to time such as the amount of horizontal or vertical distance traveled over time.
They tried out their newly acquired knowledge by creating their own paper footballs and launching them in small groups. Then they ran timed-trials to find data points that allowed them to solve for the equation of their individual parabolas. With this information, they were tasked to find the highest point their footballs reached, as well as the initial velocity that their flick provided.
To give them more real-world experience, the class moved to the basketball court where the students ran timed-trials on their own free throws and three-point shots. Again, the students could use this information to create their own equations. With these equations, the students could find the highest point the ball traveled as well as the time it would take to get there. Mr. Nestor remarked, “This exercise was a twofer! My students not only learned about parabolas but they improved their jump shots.”