Graphing the Average Rate of Change of Polynomials

Miacademy & MiaPrep Learning Channel

This educational mathematics video introduces the concept of "Average Rate of Change" by connecting it to the familiar concept of slope. The instructor, Randy, begins with a real-world application using a graph of COVID-19 infection rates from 2020-2021. By drawing a line connecting two points on the fluctuating curve, he demonstrates how to calculate the average daily increase in cases over a three-month period, effectively translating complex real-world data into a understandable linear rate. The video then transitions from data analysis to abstract algebra, using a quadratic polynomial graph ($y = x^2 + 2x$) to practice finding average rates of change over specific intervals. Through three distinct examples, the instructor guides viewers on how to identify coordinates on a curve, draw a secant line (straight line connecting two points), and calculate the slope using the rise-over-run method. The examples cover scenarios resulting in negative slope, zero slope, and positive slope, providing a well-rounded practice set. This resource is highly valuable for Algebra I and Algebra II classrooms as it bridges the gap between linear functions and non-linear functions. It visually reinforces that while curves do not have a constant slope, an "average" slope can be determined between any two points. Teachers can use this video to introduce the geometric concept of the secant line or to demonstrate how mathematical concepts like slope are used to interpret trends in real-world statistical data.