4. Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x

5. Completing the Square x 2 xxxxxx

6. Completing the Square The picture is now x 2 + 6x + 9, How many units are required to complete the square? which factors (x+3)(x+3) = (x+3) 2 9!

7. x2x2 x x x xxx 1 1 1 11 1 1 1 1

8. Let’s Try Another One! Show me x 2 + 2x x 2 xx

9. Completing the Square x 2 How many units are required to complete the square? x 2 The picture is now x 2 + 2x + 1 which factors (x+1)(x+1) = (x+1) 2 1!

10. Last One with Manipulatives Show me x 2 + 8x x 2 xxxxxxxx

11. Completing the Square Again, how many units are required to complete the square? 16 So, the picture is now x 2 + 8x + 16 which factors (x+4)(x+4) = (x+4) 2

20. Hard One! Complete the square for x 2 + 18x + ___ How many units are needed? There are not enough pieces to do this problem. Can we do it using paper and pencil?