Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x.
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Transcript of Completing the Square This is an x.Show me x 2. x x 2 Show me x 2 + 6x.
Completing the Square
This is an x. Show me x2.
x x2
Show me x2 + 6x
Completing the Square
x2
x2
x x xx x x
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!
x2xxx
x x x
1
1
1
1 1
1
1
1
1
Let’s Try Another One!
Show me x2 + 2x
x2 x x
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!
Last One with Manipulatives
Show me x2 + 8x
x2 x xx x x x x x
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
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?
