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Madotsuki

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Sep 12th, 2012
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  1. Completing the square for f(x) = x^2- 4x +2
  2. x^2- 4x + 2 = x^2- 4x + ( ) - ( ) + 2
  3.  
  4. where ( ) is half of the coefficient of x term squared
  5. x^2- 4x + 2 = x^2- 4x + (-4/2)^2- (-4/2)^2+ 2
  6. = { x^2- 4x + (-2)^2} - (-2)^2+ 2
  7. = { (x -2)^2} - 4 + 2
  8. = (x -2)^2 - 2
  9.  
  10. Completing the square for f(x) = -2x^2+7x+1
  11.  
  12. -2x^2 +7x + 1 = -2(x^2 - 7/2x - 1/2)
  13.  
  14. -2(x^2 - 7/2x + 1/2) = -2(x^2 - 7/2x + ( ) - ( ) - 1/2)
  15.  
  16. where ( ) is half of the coefficient of x term squared
  17. -2(x^2 - 7/2x + 1/2) = -2(x^2 - 7/2x + (-7/4)^2 - (-7/4)^2 - 1/2)
  18. = -2({x^2 - 7/2x + 49/16} - 49/16 - 1/2)
  19. = -2({x - 7/2}^2 - 57/16)
  20. = 57/8 - 2(x - 7/2)^2
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