Solving Real-World Problems with Factored Quadratic Functions

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide on how to use factored forms of quadratic functions to solve real-world word problems. The lesson connects abstract algebraic concepts—like factoring, finding roots, and identifying vertices—with practical applications such as calculating electrical power, tracking distance over time during a run, and determining profit margins for a business. The instructor, Justin, uses three distinct examples to demonstrate how converting standard quadratic equations into factored form reveals critical data points like x-intercepts and lines of symmetry. The video explores key themes of quadratic optimization and graphical interpretation. It specifically focuses on how to identify the maximum or minimum values (vertices) and zeros (roots) of a function to answer specific questions about physical or economic scenarios. A significant portion of the video is dedicated to visualizing these algebraic solutions on a coordinate plane, helping students see the geometric relationship between the equation and the real-world narrative it represents. For educators, this video is a valuable resource for bridging the gap between mechanical factoring skills and critical thinking in Algebra. It models how to deconstruct a word problem, formulate a mathematical approach, and interpret the results. It is particularly useful for demonstrating why finding the vertex is essential for optimization problems and how roots relate to starting and ending points in time-based scenarios. The inclusion of a "pause and solve" opportunity allows for formative assessment within the lesson flow.