Finding X and Y Intercepts Algebraically for Linear and Quadratic Functions

Mashup Math

This educational video provides a comprehensive tutorial on understanding and calculating x and y intercepts for both linear and quadratic functions. The lesson begins by visually defining intercepts on a coordinate plane, establishing the fundamental rule that the opposite coordinate is always zero (e.g., y is zero at an x-intercept). It uses color-coded points to reinforce this concept before moving into algebraic methods. The video covers key mathematical themes including coordinate geometry, linear equations in slope-intercept form, and quadratic functions. It explicitly demonstrates how to substitute zero into functions to solve for intercepts. For the linear example ($y = 3x - 6$), it uses basic inverse operations. For the quadratic example ($y = x^2 + 5x + 6$), it demonstrates how to factor a trinomial to find two distinct x-intercepts, introducing the concept that non-linear functions can cross the axis multiple times. This resource is highly valuable for Algebra I and II classrooms as it bridges the gap between graphical understanding and algebraic manipulation. Teachers can use it to introduce the concept of intercepts, review factoring quadratics, or reinforce the connection between a function's equation and its graph. The step-by-step walkthroughs serve as excellent models for student procedural practice.