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Completing the square

May 6, 2019

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

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