Completing the Square

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Completing the Square
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What is completing the square used for?

• Completing the square is used for all those not
  factorable problems!!
• It is used to solve these equations for the
  variable.

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Rule for Completing the Square
This is now a PTS!
So, it factors into this!
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Example Find the value of c that makes this a
PTS, then write the expression as the square of
a binomial. x2-3xc

• b-3

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Example Solve by completing the square.
x26x-80

• x26x-80
• x26x8
• x26x___8___
• x26x989
• (x3)217

Dont forget Whatever you add to one side of an
equation, you MUST add to the other side!
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More Examples!

• 5x2-10x300
• x2-2x60
• x2-2x-6
• x2-2x__-6__
• x2-2x1-61
• (x-1)2-5

• 3x2-12x180
• x2-4x60
• x2-4x-6
• x2-4x__-6__
• x2-4x4-64
• (x-2)2-2

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Last Example! Write the quadratic function
yx26x16 in vertex form. What is the vertex
of the functions graph?

• yx26x16
• y-16x26x
• y-16__x26x__
• y-169x26x9
• y-7(x3)2
• y(x3)27

• If the equation, in vertex form, is y(x3)27,
  then the vertex must be (-3,7).