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Math Help - complete the square

  1. #1
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    Please Help!

    Complete the square and explain how to transform the graph of y=x^2 into the graph of the given function.

    f(x)=x^2+4x+6
    Last edited by Math Help; August 22nd 2005 at 11:35 PM.
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  2. #2
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    To complete the square on ax^2 + bx + c.
    Firstly take out the coefficient of x^2 as a factor: a(x^2 + (b/a)x + (c/a)).
    Next write the square of x plus half the coefficient of the x term: (x+b/2a)^2
    Then add and subtract the constant term of that: b^2/4a^2: a((x+b/2a)^2 + c/a-b^2/4a^2)
    Then simplify: a((x+b/2a)^2 - (b^2-4ac)/4a).

    In your case: a=1
    x^2+4x+6 = (x+2)^2 + (6-4) = (x+2)^2 + 2.
    The relation between the graph of y = x^2 and the graph of y = (x+2)^2 + 2
    is a left shift of 2 (x -> x+2) and an upward shift of 2.
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