7.12 notes a
TRANSCRIPT
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Opener: Write the following expressions as products.
1.) x2 ‐ 12x + 35 2.)x4 ‐ 12x2 ‐ 64
3.)x2 ‐ 5x ‐ 84 4.) x2 ‐ 8x ‐ 20
5.) x4‐196y2 6.) ‐256 +81x20
Please get out your rough drafts & writing assignment sheets for the progress check.
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Homework Questions:
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Section 7.12 Factoring by Completing the SquareTopic One:
Factoring by Completing the Square
We can solve x2 ‐ 9 =0 using DOTS.
We can solve (x+4)2 ‐ 9 = 0 also using DOTS.
How could we use DOTS for (x ‐ 5)2 ‐ 7 = 0?
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Topic One:
Factoring by Completing the Square
What does it mean to complete the square?
What is a perfect square trinomial?
Section 7.12 Factoring by Completing the Square
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Topic One:
Factoring by Completing the Square
Solve x2‐ 66x = ‐945 by completing the square.
Completing the Square ‐ DOTSStep One: Get the equation in Normal Form and equal to zero.
Step Two: Half the coefficient of x. Square your result and add it to the first two terms.
Step Three: Rewrite your polynomial using DOTS and by fixing the constant term.
Step Four: Solve using ZPP.
(Ex. 1)
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Topic One:
Factoring by Completing the Square
Solve x2‐ 66x = ‐945 by completing the square.
Completing the Square ‐ Square Root
Step One: Get the constant alone on one side of equation.
Step Two: Build a perfect square trinomial. (* Be careful to add new constant to BOTH sides of the equation!)
Step Three: Solve your equation.
(Ex. 1)
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Topic One:
Factoring by Completing the Square
Solve x2 + 120 = 23x by completing the square. (Ex. 2)
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Topic One:
It's Your Turn!!! Solve each of the following quadratics using completing the square.
x2 + 19x + 84 = 0 x2 ‐ 8x + 15 = 0 (Ex. 3 & 4)
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Topic Two:
Quadratic Solutions
Will types of solutions can we expect when solving quadratics?
Solve each of the following using completing the square.
x2 ‐ 24x = ‐ 200
x2 + 24x + 42 = 0
x2 ‐ 12x + 45 = 0
(Ex. 5)
(Ex. 6)
(Ex. 7)
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Topic Two:
Quadratic SolutionsFor what values of c does x2 ‐ 66x + c = 0 have the following results?
a. two distinct integer solutions
b. only one integer solutions
c. no integer solutions
For what values of c does x2 ‐ 35x + c = 0 have the following results?
a. one distinct solution
b. only one solution
c. no Real number solutions
(Ex. 8)
(Ex. 9 )It's Your Turn!!!
Discuss Ex. 9 with your partner.
Let's apply our findings from before to these examples.
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Homework: • Pg. 666 # 1, 2, 5, 7, 14, 20, 22 (as is on assignment sheet)• Study for 7.11 Mini Quiz• Rough Draft # 2 for Writing Assignment 2
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