April 12, 2013              Today:                 Warm-Up: Review for Final Exam                 Solving Quadratic Equa...
Reminders:         •Khan Academy Topics for Sunday                •Final Exam Tuesday                  •At theV6Math site:...
Warm-Up/Final Exam Review:          Poly Questions about Polynomials1. Name two Polynomial sub sets: Monomials, Binomials2...
Warm-Up/Final Exam Review:Adding, Subtracting Polynomials                 What is the degree of the                  resul...
Warm-Up/Final Exam Review:
Solving Quadratic Equations by    Completing the Square:
Solving Quadratic Equations by                Completing the Square:1. So far, we have learned three different methods for...
Solving Quadratic Equations by                Completing the Square: So there are times when we could use that extra tool ...
x Example 1: x2=+-3 ±-√11 0  + 3 = ± √11;    6x 2 =     x2 + 6x = 2  x2 + 6x + 9 = 2 + 9    (x + 3) 2 = 11
x + 4 = ± 2√3; x 2 + 8x + 4 = 0  Example 2: x = -4 ± 2√3      x2 + 8x = - 4 x2 + 8x + 16 = - 4 + 16     (x + 4) 2 = 12
Example 3: x2 - 10x + 20 = 0      x = 5 ± √5
Another Way to View the Process....where....              and....Example 2: x2 + 8x + 4 = 0              d = 8/2 = 4 and  ...
Solving Quadratic Equations by                Completing the Square:There are only slight differences between the twometho...
Class WorkCompleting the Square Handout:Work with a partner if you like           #s: 4-18
x²+6x -30x²+4x-8x²+16x-27x²-10x-36x²-3x-9
where....   and....
April 12
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April 12

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April 12

  1. 1. April 12, 2013 Today: Warm-Up: Review for Final Exam Solving Quadratic Equations by Completing the Square Class Work
  2. 2. Reminders: •Khan Academy Topics for Sunday •Final Exam Tuesday •At theV6Math site:•Lots of practice questions, unit quizzes, study guides and every class days activities for download.
  3. 3. Warm-Up/Final Exam Review: Poly Questions about Polynomials1. Name two Polynomial sub sets: Monomials, Binomials2. The suffix nomial means what?3x, 3x + 2, 3x2 + 2x - 5 Terms Is it a Monomial?3. Write 3 actual monomials
  4. 4. Warm-Up/Final Exam Review:Adding, Subtracting Polynomials What is the degree of the resulting polynomial? What is the degree of the resulting polynomial?
  5. 5. Warm-Up/Final Exam Review:
  6. 6. Solving Quadratic Equations by Completing the Square:
  7. 7. Solving Quadratic Equations by Completing the Square:1. So far, we have learned three different methods forsolving quadratic equations. Name them.By factoring, By Graphing, and by Square RootsToday were going to learn a 4th way to solve quadraticequations. Were adding a too to our toolbox for thosetimes when its needed.Can we solve x2 + 8x + 7? Yes No Maybe (x + 7)(x + 1)Can we solve 8x2 - 22x + 12? Yes No MaybeWhat about 48x2 + 22x - 15? Yes No Maybe
  8. 8. Solving Quadratic Equations by Completing the Square: So there are times when we could use that extra tool to solve certain quadratic equations. This method is called completing the Square.Completing the square takes a trinomial that is not aperfect square, and turns it into a perfect squaretrinomial by adding the correct constant term.
  9. 9. x Example 1: x2=+-3 ±-√11 0 + 3 = ± √11; 6x 2 = x2 + 6x = 2 x2 + 6x + 9 = 2 + 9 (x + 3) 2 = 11
  10. 10. x + 4 = ± 2√3; x 2 + 8x + 4 = 0 Example 2: x = -4 ± 2√3 x2 + 8x = - 4 x2 + 8x + 16 = - 4 + 16 (x + 4) 2 = 12
  11. 11. Example 3: x2 - 10x + 20 = 0 x = 5 ± √5
  12. 12. Another Way to View the Process....where.... and....Example 2: x2 + 8x + 4 = 0 d = 8/2 = 4 and e = 4 - (64/4) 16 = -12Therefore, (x + 4)2 - 12 = 0; = (x + 4)2 = 12 x + 4 = ± 2√3; x = -4 ± 2√3
  13. 13. Solving Quadratic Equations by Completing the Square:There are only slight differences between the twomethods and both yield the same result. Try them bothuntil you are comfortable with one. In either case, youmust memorize the steps involved. As usual, focus noton the math, but on the process.Right now we are only going to work on equationswhere the a coefficient is 1. Monday we will work withthose equations whose coefficients are > 1.
  14. 14. Class WorkCompleting the Square Handout:Work with a partner if you like #s: 4-18
  15. 15. x²+6x -30x²+4x-8x²+16x-27x²-10x-36x²-3x-9
  16. 16. where.... and....

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