completing the square this is an x.show me x 2. x x 2 show me x 2 + 6x
TRANSCRIPT
![Page 1: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/1.jpg)
![Page 2: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/2.jpg)
![Page 3: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/3.jpg)
![Page 4: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/4.jpg)
Completing the Square
This is an x. Show me x2.
x x2
Show me x2 + 6x
![Page 5: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/5.jpg)
Completing the Square
x2
x2
x x xx x x
![Page 6: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/6.jpg)
Completing the Square
The picture is now x2 + 6x + 9,
How many units are required to complete the square?
which factors (x+3)(x+3) = (x+3)2
9!
![Page 7: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/7.jpg)
x2xxx
x x x
1
1
1
1 1
1
1
1
1
![Page 8: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/8.jpg)
Let’s Try Another One!
Show me x2 + 2x
x2 x x
![Page 9: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/9.jpg)
Completing the Square
x2
How many units are required to complete the square?
x2
The picture is now x2 + 2x + 1
which factors (x+1)(x+1) = (x+1)2
1!
![Page 10: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/10.jpg)
Last One with Manipulatives
Show me x2 + 8x
x2 x xx x x x x x
![Page 11: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/11.jpg)
Completing the Square
Again, how many units are required to complete the square?
16
So, the picture is now x2 + 8x + 16
which factors (x+4)(x+4) = (x+4)2
![Page 12: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/12.jpg)
![Page 13: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/13.jpg)
![Page 14: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/14.jpg)
![Page 15: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/15.jpg)
![Page 16: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/16.jpg)
![Page 17: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/17.jpg)
![Page 18: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/18.jpg)
![Page 19: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/19.jpg)
![Page 20: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/20.jpg)
Hard One!
Complete the square for x2 + 18x + ___
How many units are needed?
There are not enough pieces to do this problem.
Can we do it using paper and pencil?
![Page 21: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/21.jpg)
![Page 22: Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x](https://reader035.vdocuments.us/reader035/viewer/2022062313/56649cee5503460f949bb91e/html5/thumbnails/22.jpg)