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Math Help - Need help finding the range of a function

  1. #1
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    Need help finding the range of a function

    The problem is h(x) = x^2 + 8x
    I know the domain is all real. But did I solve for x correctly?

    I have set up the problem:
    y = x^2 + 8x
    y = x(x + 8)
    y/x = x + 8
    y/x - 8 = x
    y-8 = x^2
    x = square root y - 8

    But I don't get how they got the answer of x is greater than or equal to -16. Please help me.
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  2. #2
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    complete the square ...

    y = x^2 + 8x

    y + 16 = x^2 + 8x + 16

    y + 16 = (x + 4)^2

    y = (x+4)^2 - 16

    the parabola's vertex is located at (-4, -16) , therefore the range is y \ge -16
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