Using Graphs to Solve Real-World Problems

Miacademy & MiaPrep Learning Channel

This instructional video demonstrates how to solve real-world mathematical word problems by interpreting graphs rather than performing complex algebraic calculations. The narrator guides viewers through two distinct examples: a system of exponential equations representing investment growth, and a quadratic function representing agricultural yield based on rainfall. The video emphasizes visual analysis skills, teaching students to identify intersection points for comparison problems and vertex points for optimization problems. Key themes include the graphical representation of systems of equations, exponential growth models, and quadratic optimization. The video breaks down how to translate narrative information into graphical features, specifically focusing on the meaning of coefficients in exponential functions and the interpretation of axes in real-world contexts. It connects abstract mathematical functions (f(t) and g(t)) to concrete scenarios like money in a bank account or crops in a field. This resource is highly valuable for Algebra and Pre-Calculus classrooms as it bridges the gap between algebraic modeling and graphical interpretation. It helps students visualize abstract concepts, making them more accessible. Teachers can use this video to introduce the concept of systems of equations, to reinforce the skill of extracting data from graphs, or to demonstrate practical applications of finding maxima and minima in functions without using calculus.