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Math Help - Finding the intersection between two graphs

  1. #1
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    Finding the intersection between two graphs

    Hello there!

    F(x,y) = (s, -s² + 4s)
    S(x,y) = (8 -4*t, t)

    Given the two graphs F and S, find all intersections between them.

    Suggestions?
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  2. #2
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    Quote Originally Posted by ManyTimes View Post
    Hello there!

    F(x,y) = (s, -s² + 4s)
    S(x,y) = (8 -4*t, t)

    Given the two graphs F and S, find all intersections between them.

    Suggestions?
    They intersect where F(x,y) = S(x,y).

    i.e.

    (s, -s² + 4s)=(8 -4*t, t)

    i.e.

    s = 8 - 4*t (1)
    t = -s² + 4s (2)

    These are a pair of simultaneous equations, so you should be able to solve them. (Hint: Start by substituting equation (2) into equation(1), and using the quadratic formula to solve for s. Once you've done that, substitute your values for s into equation (1) or (2) to get values for t. Then use these values of s and t in the graph equations to find the points.
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  3. #3
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    Of course I should be able to solve this "problem", it is fairly easy, but I am not? I have no idea on what to do!

    So far:
    I set them as functions;
    f(x) = -s² + 4s
    g(y) = 8-4t

    Solve equations:
    x= s
    y = -x² + 4x
    y = -(x² -4x + 4) +4
    y = -(x-2)² +4

    Second equation (g(y))
    y = t
    x = 8-4y
    4y = -x+8
    y = -1/4x+2

    Then hmm what
    Last edited by ManyTimes; March 2nd 2010 at 10:40 AM.
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