How to Translate Parabolas Vertically and Horizontally

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide to translating quadratic functions on a coordinate plane. Starting with the concept of the "parent graph" (f(x) = x²), the instructor demonstrates how modifying the equation results in visual shifts. The video covers vertical translations (moving the graph up and down) and the more counter-intuitive horizontal translations (moving the graph left and right), utilizing dynamic animations to show exactly how the parabola's position changes relative to the origin. A significant portion of the lesson focuses on understanding the vertex form structure, specifically the role of variables 'h' and 'k'. The narrator places special emphasis on the common point of confusion for students: why adding a positive number inside the parentheses moves the graph to the left (negative direction) rather than the right. By teaching students to rewrite equations to reveal hidden negatives (e.g., rewriting x+3 as x-(-3)), the video provides a reliable method for determining the correct direction of the shift. For educators, this resource serves as an excellent introduction or review of quadratic transformations within an Algebra curriculum. It moves beyond rote memorization by providing conceptual justifications for the rules of graphing. The video concludes with a "test yourself" opportunity where students can pause and predict the translation of a new function, making it an interactive tool for formative assessment in the classroom.