Determining Quadratic Equations from Graphs

The Organic Chemistry Tutor

This educational video provides a clear, step-by-step tutorial on how to derive the equation of a quadratic function directly from a graph. It addresses two distinct scenarios that students commonly encounter: the first where the vertex and one other point are identifiable, and the second where the vertex is unknown but three distinct points on the curve are given. The narrator demonstrates the algebraic procedures for both situations, transitioning from visual data to precise mathematical formulas. The content explores key algebraic themes including the Vertex Form and Standard Form of quadratic equations, substitution methods, and solving systems of linear equations. It specifically highlights how to calculate the stretch factor 'a', how to expand binomials to convert between forms, and how to use the elimination method to solve for variables in a system of equations. The video emphasizes the relationship between the graphical features of a parabola (like intercepts and vertices) and the coefficients in its equation. For the classroom, this video is an excellent resource for Algebra I, Algebra II, and Pre-Calculus units on quadratic functions. It bridges the gap between graphing and algebraic manipulation, helping students understand that graphs and equations are interchangeable representations of the same data. Teachers can use the two distinct examples to differentiate instruction—using the vertex method for introductory lessons and the three-point method for advanced lessons on systems of equations and curve fitting.