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Math Help - Finding domain and range of a function without graphing it

  1. #1
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    Finding domain and range of a function without graphing it

    Hi, how can I find the domain and range of this function without graphing:

    f(x) = x^2 - 6x - 10

    I know domain is x is any real number..How do i find the range
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  2. #2
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    Quote Originally Posted by jsaroya View Post
    Hi, how can I find the domain and range of this function without graphing:

    f(x) = x^2 - 6x - 10

    I know domain is x is any real number..How do i find the range
    Find the vertex (where the parabola changes direction).

    If you are in Pre-Algebra and Algebra as your post location suggests, you can find the vertex by putting the equation in the form suggested here

    Parabola - Wikipedia, the free encyclopedia

    If you happen to be in Calculus and just filed this post in Pre-Algebra and Algebra by mistake, you can find the global minimum by taking the derivative and setting it to 0.
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    Yes I am in Pre-algebra. So I convert it into vertex form using something like the completing the square method?
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    You are right, completing the square is the standard way to solve this using elementary methods, unless you have memorized the formula x = -b/(2a). Here is a link that's rather easier to follow than Wikipedia and shows worked examples.

    Vertex of a Parabola

    (Scroll down a bit to where it discusses general equations of the form x = ax^2 + bx + c.)

    If you have any questions feel free to post again.
    Last edited by mr fantastic; September 10th 2010 at 04:12 AM.
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    Thank you!
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