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Math Help - An expression representing the following function...

  1. #1
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    An expression representing the following function...

    So I'm stuck on this question: find an expression for the function whose graph is the bottom half of the parabola, x+(y-3)^2=0. It should be expressed in terms of x according to the text that I'm working from.

    The problem I'm having is actually isolating y without encountering a negative square root...Now, I haven't learned how to deal with complex numbers much so I'm not sure if that's the only way to do this. If it's possible to do this normally, could I have some hints?
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  2. #2
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    If you're expressing it in terms of x then

    x = -(y - 3)^2.
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    Oops, I meant expressing it as y in terms of x so that's it's y=
    Last edited by VectorRun; September 24th 2010 at 07:19 PM.
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    (y - 3)^2 = -x

    y - 3 = \pm \sqrt{-x}

    y = 3 \pm \sqrt{-x}.


    If you want the lower half then only accept

    y = 3 - \sqrt{-x}.
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    Oh, is that really an acceptable answer? I got that but I wasn't sure if it was right due to the negative radicand...I guess I got thrown off by all the teachers always saying it's a big no-no. Thanks a lot.
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  6. #6
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    Is -x always a negative number?
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    I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.
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    Quote Originally Posted by VectorRun View Post
    I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.
    Doesn't matter, there's such a thing as an implied domain. There's nothing wrong with the notation as long as it's possible for any value of x.
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