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Math Help - Hyperbola

  1. #1
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    Hyperbola

    (y+1)^2/4 - (x-2)^2/16 = 1

    so i know how to graph it....

    i know the center is (-1,2)

    Am I right the to say the a-value is 2 or is it +and- 2
    and the b-value is 4 or is it +and- 4

    and finally how do you find the domain and range?

    is the range 0 less than or equal to y greater than or equal 4
    and the domain all real?
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  2. #2
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    Quote Originally Posted by zooanimal98 View Post
    (y+1)^2/4 - (x-2)^2/16 = 1

    so i know how to graph it....

    i know the center is (-1,2)

    Am I right the to say the a-value is 2 or is it +and- 2
    and the b-value is 4 or is it +and- 4

    and finally how do you find the domain and range?

    is the range 0 less than or equal to y greater than or equal 4
    and the domain all real?
    a = 4, b = 2. If you draw the graph (which you say you can do) the domain and range will be obvious.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    a = 4, b = 2. If you draw the graph (which you say you can do) the domain and range will be obvious.
    obviously it is not obvious for me. i am staring at the graph in front of me... i looks like to wide u's, one facing up, one facing down...what I don't see is the domain and range...

    do you know how to find it?
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  4. #4
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    Quote Originally Posted by zooanimal98 View Post
    obviously it is not obvious for me. i am staring at the graph in front of me... i looks like to wide u's, one facing up, one facing down...what I don't see is the domain and range...

    do you know how to find it?
    The domain is all real numbers.

    The range is \{ y : ~ - \infty < y \leq y_1 \} \cup \{ y : ~ y_2 \leq y < \infty \} where y_1 and y_2 are the y-coordinates of the maximum and minimum turning points respectively.

    Do you know how to find the coordinates of the turning points (which are key features that should be labelled on your graph)?
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  5. #5
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    Range

    are the coordinates (-1,4) and (-1,0)?

    so then range is (- infty < y less than or equal to 4)
    ( 0 < y less than or equal to infty)

    ok is that wrong...

    Quote Originally Posted by mr fantastic View Post
    The domain is all real numbers.

    The range is \{ y : ~ - \infty < y \leq y_1 \} \cup \{ y : ~ y_2 \leq y < \infty \} where y_1 and y_2 are the y-coordinates of the maximum and minimum turning points respectively.

    Do you know how to find the coordinates of the turning points (which are key features that should be labelled on your graph)?
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  6. #6
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    Quote Originally Posted by zooanimal98 View Post
    are the coordinates (-1,4) and (-1,0)?

    so then range is (- infty < y less than or equal to 4)
    ( 0 < y less than or equal to infty)

    ok is that wrong...
    No.

    (2, 1) and (2, -3).

    Draw \frac{y^2}{4} - \frac{x^2}{16} = 1 and apply the necessary translations.

    And by the way, the centre is at (2, -1)

    so i know how to graph it....
    Not until you can correctly find the vertices and centre you do ....
    Last edited by mr fantastic; August 18th 2008 at 02:26 PM.
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    No.

    (2, 1) and (2, -3).

    Draw \frac{y^2}{4} - \frac{x^2}{16} = 1 and apply the necessary translations.

    And by the way, the centre is at (2, -1)


    Not until you can correctly find the vertices and centre you do ....
    so sorry that I accidentaly switched y for x when I was graphing. Thanks for the help, btw you are not fantastic.
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