Welcome to this deck on completing the square. This is a powerful technique in algebra for rewriting a quadratic expression. Instead of the usual 'x squared plus bx plus c' form, we'll turn it into a new form that makes it much easier to find the turning point of its graph.

The name 'completing the square' gives a big clue. We're trying to make a perfect square. For example, if you expand the expression 'x plus 3, all squared', you get 'x squared plus 6x plus 9'. This is called a perfect square trinomial.

Now, let's take an expression that isn't a perfect square, like 'x squared plus 6x plus 5'. The first part, 'x squared plus 6x', looks like the start of our 'x plus 3, all squared' expression. We can use this to build our completed square form.

The first step is always to look at the number multiplying the x term, which we call the coefficient. To decide what goes inside our squared bracket, we simply halve this coefficient.