Completing the Square and Finding the Vertex

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Completing the Square and Finding the Vertex
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Perfect Square

• A polynomial that can be factored into the
  following form
• (x a)2
• Examples

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Completing the Square

• x2 bx c is a perfect square if
• (The value of c will always be positive.)
• Ex Prove the following is a perfect square

Half of b-16 squared is 64c
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Completing the Square

• Find the c that completes the square
• x2 50x c
• x2 22x c
• x2 15x c

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Factoring a Completed Square

• If x2 bx c is a perfect square, then it will
  easily factor to
• Ex Prove the following is a perfect square.

Half of b8 is 4
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Perfect Squares Parabolas Circles

• Find the vertices of the following graphs and
  state whether they are maximums or minimums.
• y (x 5)2 5
• y -(x 3)2 1
• y -3(x 7)2 8
• y 4(x 52)2 74
• State the length of the radius and the
  coordinates of the center for each circle below
• ( x 2 )2 ( y 7 )2 64
• x2 y2 36
• ( x 4 )2 ( y 11 )2 5
• ( x 3 )2 y2 175

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Standard to Graphing Quadratic
Find the vertex of the following equation by
completing the square
Find the c that completes the square

• y x2 8x 25

GOAL
y a ( x h )2 k
Plus a box, minus a box
Complete the Square
y (x2 8x ) 25
y (x2 8x ) 25
16
16
Factor what is in the Parentheses
y (x 4)2
9
Simplify
(-4, 9)
Vertex
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Standard to Graphing Quadratic
Find the vertex of the following equation by
completing the square

• y 3x2 18x 10

GOAL
y a ( x h )2 k
y 3(x2 6x ) 10
3
9
9
y (x 3)2
3 10 27
y 3(x 3)2 37
(3,-37)
Vertex
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A new Equation?

• What will the graph of the following look like

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Standard to Graphing Circle
Find the center and radius of the equation by
completing the square

• x2 y2 6x 12y 9 0

Arrange similar variables together
x2 6x y2 12y 9 0
Isolate the terms with variables
9 9
x2 6x y2 12y 9
Complete the square twice
(x2 6x ) (y2 12y ) 9
36
9
9
36
(x 3)2
(y 6)2
54
(-3, 6)
Center Radius