Finding the Equation of a Quadratic Function Given Three Points

The Organic Chemistry Tutor

This educational video provides a step-by-step tutorial on how to determine the equation of a quadratic function in standard form ($y = ax^2 + bx + c$) when given specific coordinates that the parabola passes through. The narrator demonstrates two distinct types of problems: one where the y-intercept is explicitly provided, simplifying the process, and a more complex scenario where three arbitrary points are given, requiring the solution of a system of three linear equations with three variables. The video explores key algebraic themes including quadratic functions, standard form, and systems of linear equations. It emphasizes the method of substitution to generate equations and the elimination method to solve for the unknown coefficients ($a, b, c$). The content highlights the importance of precision in algebraic manipulation and demonstrates self-correction strategies when the narrator catches and fixes a calculation error in real-time. For educators, this video is an excellent resource for Algebra 2 or Pre-Calculus classrooms. It models the procedural thinking required for solving systems of equations in the context of curve fitting. Teachers can use it to demonstrate how geometric points translate into algebraic constraints, or as a reference for students struggling with the lengthy process of solving 3x3 systems. The 'live' error correction also serves as a valuable teaching moment about the necessity of double-checking mental math.