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Math Help - Points of Intersection between Parabola and Exponential Graph

  1. #1
    dogdirt2000
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    Points of Intersection between Parabola and Exponential Graph

    Hi, i haven't done any strong maths since i left college 2 years ago, and have just been going over some of the notes and hand-outs i received just out of curiosity. One question in my notes, however, has really stumped me - it's probably cos i'm a little rusty after not doing it for so long.

    Basically, the question is the find the points of intersection between two graphs, where one of them is an exponential function.

    first graph is y = 3e^-x
    second graph is y = 12x^2 - 1

    so, 3e^-x = 12x^2 - 1

    I know the points of intersection are actually x = -0.7997 & x= 0.4868
    I just get stuck half-way through working it out!

    Any advice would be great

    Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dogdirt2000 View Post
    Hi, i haven't done any strong maths since i left college 2 years ago, and have just been going over some of the notes and hand-outs i received just out of curiosity. One question in my notes, however, has really stumped me - it's probably cos i'm a little rusty after not doing it for so long.

    Basically, the question is the find the points of intersection between two graphs, where one of them is an exponential function.

    first graph is y = 3e^-x
    second graph is y = 12x^2 - 1

    so, 3e^-x = 12x^2 - 1

    I know the points of intersection are actually x = -0.7997 & x= 0.4868
    I just get stuck half-way through working it out!

    Any advice would be great

    Thanks.
    You are going to have to do this numerically. You might be able to find a way to use the Lambert(?) function to give an explicit notation for them.

    For the record there are 3 solutions, not 2:
    x = 0.486806, -0.79973, -4.29814

    -Dan
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