Completing The Square Using Algebra Tiles Worksheet Page 3
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1
2
3
4Represent each expression by sketching algebra tiles. Try to create a square of tiles. When doing so
keep the following rules in mind:
• You may only use one x
2
-tile in each square.
• You must use all the x
and x-tiles. Unit tiles are the only ones that can be leftover or
2
borrowed.
• If you need more unit tiles to create a square you have to “borrow” them. The number you
borrow will be a negative quantity.
4.5.1 Completing the Square – Algebra Tile Investigation
(continued)
Area of the
Expression
Standard
Number
Number
Number
Length of
Unit Tiles
Square
Combining
2
Form
of x
of x
of Unit
the
Left Over (+)
Sketch of the Square
2
(Length)
Previous Two
Tiles
Tiles
Tiles
Square
Borrowed (-)
Columns
2
2
2
(x+1)
(x+1)
+ 2
x
+ 2x + 3
1
2
3
x+1
2
2
x
+ 4x + 1
+ 6x +10
2
2
x
x
+ 6x + 8
Grade 11 U/C – Unit 4: Quadratic - Highs and Lows
22
12. What is the name of the form for the combined expression in the last column?
Convert the following equations from standard form to vertex form by completing the square.
13. y = x
− 8x +11
14. y = x
+16x +14
2
2
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