AlgCC 4­17­17 Mod 4 Lesson 11 ­ Rewriting by Completing the Square.notebook
April 17, 2017
Objective: (Lesson 11) Rewriting Expressions by Completing the Square
Do Now:
page 1 (NEW packet)
Monday, 4.17.17
Opening Exercise:
Rewrite the following perfect square quadratic expressions in standard form. Fill in the blanks below by describing the patterns in the coefficients for the factored form, (x + a)2, and the standard form, x2 + bx + c. equivalent For each row, the factored form and standard form are _______________________ expressions, so (x + a)2 = x2 + bx + c. half of b
A, the constant in factored form of the equation, is always ___________________________, the coefficient of the linear term in the standard form. C, the constant term in the standard form of the quadratic equation, is always the square
_______________________ of the constant in the factored form, A. Now, try working backwards. Rewrite the following standard form quadratic expressions as perfect squares.
What is different about x2 + 8x + 3? Why is it impossible to factor this expression as a perfect square binomial?
It is not a perfect square. There aren't two identical factors that multiply to 3 and add to 8.
If you could change something about the last expression to make it a perfect square, what would you change?
If the constant term were a 16, it would be a perfect square (42 as the constant term and 4(2) as the b value).
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AlgCC 4­17­17 Mod 4 Lesson 11 ­ Rewriting by Completing the Square.notebook
April 17, 2017
page 2
Example: Find an expression equivalent to x2 + 8x + 3 that includes a perfect square binomial.
Exercises: Rewrite each expression by completing the square.
1. x2 – 4x + 15
2. n2 – 2n – 15 page 2
Exercises: Rewrite each expression by completing the square.
3. c2 + 20c – 40
4. y2 – 3y + 10
5. k2 + 7k + 6
6. z2 – 0.2z + 1.5
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AlgCC 4­17­17 Mod 4 Lesson 11 ­ Rewriting by Completing the Square.notebook
April 17, 2017
Problem Set (HW)
# 1 ­ 4 Show ALL work!!!
page 3
1. Rewrite the expression x2 + 4x + 3, first by factoring and then by completing the square. Which way is easier? Explain why you think so.
Examples 2 – 6: Rewrite each expression by completing the square.
2. q2 + 12q + 32
3. m2 – 4m – 5 4. x2 – 7x + 6.5 5. a2 + 70a + 1225
6. z2 – 0.3z + 0.1
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