Using Quadratic Graphs to Answer Real-World Questions

Miacademy & MiaPrep Learning Channel

This video serves as a practical guide for interpreting quadratic graphs (parabolas) within real-world contexts. Building on prior knowledge of graph shapes, the lesson focuses on extracting specific data points to answer narrative-driven questions. The presenter walks through three distinct examples: a drone flight representing height over time, a sales model maximizing profit based on price, and a business scenario tracking profit and loss over several months. By shifting perspective from abstract geometry to concrete storytelling, students learn to locate key features like intercepts, maxima (vertices), and minima to solve problems. Key themes include the interpretation of the vertex as a maximum or minimum point, understanding x-intercepts as start or end points in a timeline, and calculating intervals between events. The video distinguishes between reading a graph as a chronological story versus a cause-and-effect relationship, providing students with different mental models for analysis. It also tackles multi-step problems where the answer isn't a single point on the graph but the difference between two points, encouraging deeper critical thinking. For educators, this resource bridges the gap between abstract algebra skills and mathematical modeling. It is highly valuable for demonstrating why quadratic functions matter outside the classroom, specifically in physics and business applications. The clear, step-by-step breakdown of the "harder" example provides an excellent model for scaffolding complex word problems, helping students move beyond simple coordinate identification to analyzing relationships between variables.