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Math Help - complete the square

  1. #1
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    help with precal problems plz

    Can someone please help me figure out what I did wrong with these problems?

    1. complete the square to write the equation of the parabola f(x) = -8x^2 - 24x + 15 in (h,k) form.

    I can up with:
    -8(x-3/2)^2 -3
    ( 3/2 , -3) ... but this is wrong... I dunno why...

    2. find the domain of f(g(x))
    f(x) = 1/(x-2) g(x) = 1/(radical x-3)

    I came up with:
    1/{[1/(radical x-3)] -2 } as the equation and so i know that x ≥ -3 and i also set up the equation (radical x-3) ≠ 1/2 because 1/(1/2) is 2 and 2-2 is 0.
    so... how would I write the domain in the (x:x) = (-infinity, a number)(a number, infinity) form?

    3. find a relationship between x and y so that (x,y) is equidistant from two points (5,2) and (-1,7). solve for a simplified relationship between x and y, don't solve for x and y.

    I had no idea how to solve this one.


    Thanks for viewing my thread.
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  2. #2
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    Your -8(x-3/2)^2 = -8x^2 -8.2.(-3/2)x - 8(-3/2)^2 = -8x^2 + 24x - 18.
    You wanted -8(x+3/2)^2 which is -8x^2 - 24x - 18.
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  3. #3
    vms
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    Quote Originally Posted by u317d
    Can someone please help me figure out what I did wrong with these problems?

    2. find the domain of f(g(x))
    f(x) = 1/(x-2) g(x) = 1/(radical x-3)

    I came up with:
    1/{[1/(radical x-3)] -2 } as the equation and so i know that x ≥ -3 and i also set up the equation (radical x-3) ≠ 1/2 because 1/(1/2) is 2 and 2-2 is 0.
    so... how would I write the domain in the (x:x) = (-infinity, a number)(a number, infinity) form?
    f(g(x))=1/(g(x)-2) is defined for g(x) ≠ 2 i.e, for (radical x-3) ≠ 1/2 ie
    x ≠ 3+1/4=13/4
    and g(x) is defined only when x>3
    over all now, x has to be a number from 3 to 13/4 or 13/4 to infinity (excluding 13/4)
    which we can write as domain = {x: x belongs to (3, 13/4) U (13/4, infinity)

    Hope this clears your doubt
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by u317d
    Can someone please help me figure out what I did wrong with these problems?

    1. complete the square to write the equation of the parabola f(x) = -8x^2 - 24x + 15 in (h,k) form.
    What is (h,k) form?

    RonL
    Last edited by CaptainBlack; January 14th 2006 at 01:46 AM.
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  5. #5
    Member jacs's Avatar
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    Red face

    (h, k) usually refers to the coordinates of the vertex and the form

    (x - h) = 4a(y - k)

    y = -8x - 24x + 15

    8x + 24x = 15 - y
    x + 3x = 1/8(15 - y)

    x + 3x + 9/4 = 1/8(33 - y)

    (x + 3/2) = 1/8(33 - y)


    (h, k) = (-3/2, 33)
    Last edited by jacs; January 15th 2006 at 07:31 AM.
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