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Math Help - Manipulating quadratic functions

  1. #1
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    Manipulating quadratic functions

    Hi,

    Is it possible to manipulate a quadratic function so that it has a gradient of 35.5 at the point (1,33) while forcing it to have an x-intercept of 10 and the other x-intercept being anything less then 10. I have no idea how to approach this...
    Any help will be greatly appreciated.

    Thanks,
    John
    Last edited by deovolante; April 24th 2010 at 04:45 PM.
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  2. #2
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    Quote Originally Posted by deovolante View Post
    Hi,

    Is it possible to manipulate a quadratic function

    Let's call it ax^2+bx+c


    so that it has a gradient of 35.5 at the point (1,33)


    So a+b+c=33\,\,\,and\,\,\,also\,\,\,2a+b=35.5


    while forcing it to have an x-intercept of 10 and the other x-intercept being anything less then 10


    This means 100a+10b+c=0 and also that there must exist \alpha<10\,\,\,s.t.\,\,\,a\alpha^2+b\alpha+c=0


    . I have no idea how to approach this...
    Any help will be greatly appreciated.

    Thanks,
    John

    Now solve the linear system formed by the first three eq.'s above (it has a unique, pretty nasty, solution) , and then check ( for example, with

    the help of Viete equations) if the coefficients a,b,c you get can fulfill the last condition together with the other ones.

    Tonio
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