Completing the square

Grade 10s are getting skilled with using vertex form, and we are now learning how to change an equation into vertex form, by completing the square.

Step 1: represent the trinomial, and in this case we always want to make a square, so we split the x term in 2 groups, and use those for the sides of the square. We need to fill the square with 9 red squares. In order to get 9 red squares we need to add 9 zero pairs.

Our final equation in vertex form is y=(x-3)^2-11

Here’s another example: x^2+4x+1

We need to complete the square with 3 more red squares so we add 3 zero pairs

And complete the square

Our final form is y=(x+2)^2-3