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- Completing the square for f(x) = x^2- 4x +2
- x^2- 4x + 2 = x^2- 4x + ( ) - ( ) + 2
- where ( ) is half of the coefficient of x term squared
- x^2- 4x + 2 = x^2- 4x + (-4/2)^2- (-4/2)^2+ 2
- = { x^2- 4x + (-2)^2} - (-2)^2+ 2
- = { (x -2)^2} - 4 + 2
- = (x -2)^2 - 2
- Completing the square for f(x) = -2x^2+7x+1
- -2x^2 +7x + 1 = -2(x^2 - 7/2x - 1/2)
- -2(x^2 - 7/2x + 1/2) = -2(x^2 - 7/2x + ( ) - ( ) - 1/2)
- where ( ) is half of the coefficient of x term squared
- -2(x^2 - 7/2x + 1/2) = -2(x^2 - 7/2x + (-7/4)^2 - (-7/4)^2 - 1/2)
- = -2({x^2 - 7/2x + 49/16} - 49/16 - 1/2)
- = -2({x - 7/2}^2 - 57/16)
- = 57/8 - 2(x - 7/2)^2
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