Freshmen students at Roberto Clemente Community Academy have begun a study of the quadratic function, an equation that explains architecture, technology, and movement of objects all around us in the natural world. By using real world representations of the quadratic function in the form of the parabolic curve—found in archways, bridges, satellite dishes and even the McDonald’s arches—its properties explain the rules that govern the movement of objects through space. TTS algebraic calculation creates the foundation for GPS, cell phones, and many of the technological breakthroughs of today, and students are becoming aware of how pervasive this function is in everyday life.
Freshmen began their investigation by understanding the basic properties of the function’s graph, its key elements, and their definitions. They continued by connecting the visual to the algebraic expressions. This week they moved their exploration to understand the mathematical connections and truths behind the shape of the curve and its algebraic equation. By identifying the parts of the curve as they exist in graphic form and relating those to the function’s equation using formulas to predict the curves dimensions, our mathematicians are beginning to explore some of the basic foundations of graphic design and engineering.
After their initial analysis, the students will engage in some problem solving where they will be tasked with finding the properties and predicting the path of projectile scenarios and exploring the problem-solving strength of the quadratic model in real-world engineering situations. As they gain confidence in moving between the graphic representation and its algebraic equation, they will begin to use computer programs like Desmos to help them flesh out their calculation and give them a greater understanding of the application they are investigating.
Finally, students will be given an opportunity to develop their own short video or slide presentation of an example of the quadratic function in a real-world setting, applying all they know to showcase their mastery of understanding the application of the parabolic shape.