Applications of completing the square – sketching graphs

In these tutorials I show you how we can use completing the square to sketch a quadratic graph, locate the maximum or minimum points and the equation of the line of symmetry.

Part 1: (+ax2 types)

Part 2: (-ax2 types)

Experiment with the Graph

Move the sliders in the graph below

  1. See how p stretches the graph. See what happens for positive and negative values.
  2. See how q translates the graph parallel to the x-axis.
  3. See how r translates the graph parallel to the y-axis.