Download Aim #51 - Manhasset Public Schools

Aim #51: How do we write quadratic expressions given in standard form
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ax + bx + c (with a = 1) in the equivalent completed-square form?
Homework: Handout
Do Now: Fill in the chart. Follow the first example.
Do you see any patterns in the numbers in the first column and those in the last?
Generalize for (x + n)2
(x + n)2 = x2 + 2nx + n2
Rewrite the following as perfect squares
x2 + 12x + 36
x2 - 12x + 36
x2 + 100x + 2500
x2 + 8x + 3
x2 + 20x + 100
For x2 + 8x + 3 to factor to a perfect square, what number would we want to
have as the constant instead of the number 3?
x2 + 8x + 3 = x2 + 8x + ___ + 3 - ___
x2 + 8x + 3 =
Notice that ___ is half the middle term's coefficient squared.
Now check that the new expression is equivalent to x2 + 8x + 3
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The previous method is called __________________________.
Complete the square for the following expressions.
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2. n - 2n - 15
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2
4. x - 1000x + 60000
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6. k + 7k + 6
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8. p + 0.5p + 0.1
1. x - 4x + 15
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3. c + 20c - 40
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5. y - 3y + 10
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7. z - 0.2z + 1.5
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9. j - 3 j +
4
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3
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10. x - bx + c
LET'S SUM IT UP!
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To complete the square of a quadratic equation in standard form ax + bx + c
(a = 1) we add half the middle term's coefficient squared and we subtract half
the middle term's coefficient squared
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2
b 2
2
b 2
2
x + bx + c = x + bx + ( ) + c - ( ) = (x +
b 2
b 2
) + c - ( )
2
2
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