1. Another method to solve quadratics
Completing the square
Another method to solve quadratics

2. What does a square look like?
Is this a square?
What about this one?
This one?
Why isn’t the last picture a square?

3. Question… What would we need to do to make this a square?
Right, we would need to fill in the missing bottom section.

4. Same with quadratics We can model a quadratic expression like this
with tiles like this...
This is the
Split the x piece in 2 and put 1/2
 here
rest here
The constant (4) goes here

5. Now it’s your turn
Each group has some squares and rectangles. Practice showing completing the square for the following problems:
Write the problems on a piece of paper and fill in the blanks when you find the number of small squares needed to complete the square.
𝑥 x +____
𝑥 2 +10𝑥+ ______
𝑥 2 +6𝑥+______
𝑥 2 +12𝑥+ ______

6. What did you notice? 𝑥 2 + 8x + 16 𝑥 2 +10𝑥+25
Take 3 minutes and discuss some of the things you notice about what happened when you worked out those problems. Write your observations under the problems on the paper.
What were the answers you got for the problems
𝑥 x + 16
𝑥 2 +10𝑥+25
𝑥 2 +6𝑥+9
𝑥 2 +12𝑥+36