How to Graph Quadratic Functions in Standard Form Step-by-Step

The Organic Chemistry Tutor

This instructional math video provides a step-by-step tutorial on how to graph a quadratic function in standard form ($y = ax^2 + bx + c$). The specific example used is $y = x^2 - 4x + 3$. The narrator demonstrates a systematic approach that moves beyond simple table-building by calculating specific key features of the parabola: the vertex, x-intercepts, and y-intercept. The video covers several fundamental algebra concepts, including using the vertex formula ($x = -b/2a$), factoring quadratics to find roots, evaluating functions, and understanding parabolic symmetry. The tutorial concludes by analyzing the completed graph to identify the axis of symmetry, minimum value, domain, and range. This resource is highly valuable for Algebra students as it connects algebraic calculations directly to graphical representations. It is particularly useful for teachers introducing quadratic graphs because it explains *why* certain points are chosen for the data table rather than picking random x-values. The clear, handwritten visual style helps focus student attention on the procedural logic of graphing.