Completing the square

Here is an expression: 1x^2+6x-3

We are going to write it in vertex form by completing the square.  To make a square, we take the x term and split it in half.  Half of the x goes vertically and half horizontally.

We notice that we could complete the square with 9 little red squares.  Since we don’t have any, we need to add some zero pairs.

With 9 additional blue and red squares added, we can complete the square.

We now have a square: (x+3)^2 and also 12 blue square tiles.  The expression can now be expressed as (x+3)^2-12.