How to Graph Quadratic Functions Without a Calculator

Mashup Math

This educational video provides a clear, step-by-step guide on how to graph quadratic functions manually without relying on a graphing calculator. It begins by reviewing linear functions to establish a baseline of understanding regarding input/output tables and graphing, before transitioning to quadratic equations in standard form. The video introduces the concept of a parabola and emphasizes the critical importance of finding the vertex as the starting point for graphing quadratics, distinguishing this from the y-intercept method used for lines. The core of the video focuses on the procedural mechanics of graphing quadratics. It introduces the specific formula for finding the axis of symmetry ($x = -b/2a$) and demonstrates how to use this value to calculate the vertex's coordinates. Through two detailed worked examples, the narrator walks viewers through identifying coefficients, calculating the axis of symmetry, substituting values to find the vertex, and constructing a table of values around that central point to plot the curve accurately. This resource is highly valuable for Algebra students struggling with the procedural steps of graphing. It breaks down a complex multi-step process into manageable chunks, making it ideal for direct instruction or remediation. Teachers can use this video to flip the classroom, having students learn the method at home, or as a visual aid during a lesson to demonstrate the connection between the algebraic formula and the geometric shape of the parabola.