I am assuming that you are familiar with squaring a bracket. If not I would encourage you to look at this short video first before tackling completing the square.

In this series of three tutorials I take you through all the different types, depending on the x2 term.

Completing the square for when you get x2 terms only

Completing the square for when you get 2×2, 3×2,… terms

Completing the square for when you get -x2, -2×2,… terms

In these tutorials I show you how we can use completing the square to show prove that a quadratic expression is positive or negative for all real values and also in the sketching of quadratic graphs, enabling the location of maximum or minimum points and the equation of the line of symmetry.

Proof for Quadratic Expressions being >0 or <0

Part 1: (+ax2 types)

Part 2: (-ax2 types)

## Experiment with the Graph

Move the sliders in the graph below

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