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Math Help - intersection of two functions

  1. #1
    Junior Member
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    Jul 2008
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    intersection of two functions

    Hi,

    Could some one explain how to find the intersection of parabola y^2=x with the line y = x/4

    cheers
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  2. #2
    MHF Contributor
    Joined
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    At the intersection point, the point is common to both curves. So the (x,y) of one is also the (x,y) of the other. Hence, solve the two equations simultaneously.

    y^2 = x ---------(1)

    y = x/4
    4y = x -----------(2)

    The x of (1) is also the x of (2), so,
    y^2 = 4y
    y^2 -4y = 0
    y(y -4) = 0
    y = 0 or 4

    When y=0,
    y^2 = x
    0 = x
    So, point (0,0)

    When y = 4,
    4^2 = x
    x = 16
    So, point (16,4)

    Those two points are the intersections of the two curves (a parabola and a straight line).
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