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Math Help - function and completing square

  1. #1
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    function and completing square

    problem 1: re-arrange g(x) function below to completed square form
    g(x)=-x^2+4x+1

    I know the answer is 5-(x-2)^2

    But how to get the answer? Mind to show steps?

    problem 2: determine the turning point (x,y)
    the answer is (2,5) but how to determine which term belongs to x or y ? does the term inside the brackets of square belong to x and the constant is y as a fixed rule?

    thank you
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  2. #2
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    Quote Originally Posted by jasonmark View Post
    problem 1: re-arrange g(x) function below to completed square form
    g(x)=-x^2+4x+1

    I know the answer is 5-(x-2)^2

    But how to get the answer? Mind to show steps?

    problem 2: determine the turning point (x,y)
    the answer is (2,5) but how to determine which term belongs to x or y ? does the term inside the brackets of square belong to x and the constant is y as a fixed rule?

    thank you
    g(x) = -(x^2 -4x - 1) = -([x - 2]^2 - 2^2 - 1) = \, ....

    y = a(x - h)^2 + k has a turning point at (h, k). In your question (whose answer can be re-written as y = -(x-2)^2 + 5), h = 2 and k = 5.
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  3. #3
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    thank a lots
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