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Math Help - Point of intersection of two curves

  1. #1
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    Point of intersection of two curves

    Hi
    I am struggling with this method-my book does not explain it very well.
    Can anybody recommend a method to follow? or maybe an example on line?
    thanks
    John
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  2. #2
    Super Member Bacterius's Avatar
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    Re: Point of intersection of two curves

    Let the two curves be defined by the equations y_1 = f(x_1) and y_2 = g(x_2). The points of intersection of these two curves is defined as the solutions to the conditions x_1 = x_2 and y_1 = y_2. Substituting the curve equations into the previous equation, we get f(x_1) = g(x_2), and since x_1 = x_2, this is equivalent to f(x_1) = g(x_1). Let x_1 = x for simplicity, and it follows that solving f(x) = g(x) is equivalent to finding the x-coordinates of all the intersections between the two curves.

    So for instance if you want to find the points of intersection of the equations:

    y = x^2 + 2x - 1
    y = 2x + 3

    You will want to solve x^2 + 2x - 1 = 2x + 3, which simplifies to x^2 - 4 = 0. The solutions are therefore x = \{-2, 2\}, and substituting back these x-values into either of the curve equations will give you the y-coordinates of the points of intersection, which are y = \{-1, 7\} respectively. Thus the points of intersection are (-2, -1) and (2, 7).
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  3. #3
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    Re: Point of intersection of two curves

    thanks for your help
    John
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