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Math Help - Finding a Parabolic equation with imaginary points?

  1. #1
    Newbie AtlasSniperman's Avatar
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    Finding a Parabolic equation with imaginary points?

    I know this is a really off the wall question, and I don't know where else to put it so here goes:

    For the past 2 months I've been trying to figure out an equation for a parabolic line, I've tried all methods I can find around the internet, and several contacts have not been able to assist me.

    I need to find the equation that satisfies these three points without giving the letters set numerical values:
    (0,C) (T,100) (T+100,100)

    Any and All help would be greatly appreciated, it'd been burning my brain to find the answer to this
    Last edited by AtlasSniperman; September 19th 2012 at 03:32 AM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Finding a Parabolic equation with imaginary points?

    Let the parabola have the standard form:

    f(x)=ax^2+bx+c

    From the given points, we have the linear system:

    a(0)^2+b(0)+c=c=C

    Using this, the system reduces to:

    a(T)^2+b(T)+C=100

    a(T+100)^2+b(T+100)+C=100

    Now you may solve this system to determine (a,b) in terms of C and T.

    You will find then:

    f(x)=\frac{C-100}{T^2+100T}x^2+\frac{2(100-C)-100C+100^2}{T^2+100T}x+C
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  3. #3
    Newbie AtlasSniperman's Avatar
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    Re: Finding a Parabolic equation with imaginary points?

    This is as far as I was able to get also, however when checking it, the values simply decrease from (0,C) and do not satisfy the points (T,100) or (T+100,100), instead it appears to X intercept at ~70-80% of T, whereas it should pass through 100Y at T and again at T+100
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  4. #4
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Finding a Parabolic equation with imaginary points?

    Quote Originally Posted by AtlasSniperman View Post
    I need to find the equation that satisfies these three points without giving the letters set numerical values: (0,C) (T,100) (T+100,100)
    y(x)={C}-\frac{2 (-100+\text{C}) (50+T) x}{T (100+T)}+\frac{(-100+\text{C}) x^2}{T (100+T)}

    Attached Thumbnails Attached Thumbnails Finding a Parabolic equation with imaginary points?-parabola-equation.png  
    Last edited by MaxJasper; September 19th 2012 at 08:35 PM.
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  5. #5
    Newbie AtlasSniperman's Avatar
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    Re: Finding a Parabolic equation with imaginary points?

    YES! Thank you so very much MaxJasper, this is exactly what I was looking for, and now that I see both the answer and all the attempts I made I can see how it was done.
    Thank you again, it is GREATLY appreciated
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Finding a Parabolic equation with imaginary points?

    That's exactly what I gave you, only in a different form...
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  7. #7
    Newbie AtlasSniperman's Avatar
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    Re: Finding a Parabolic equation with imaginary points?

    I can see the the transition from your form to his, and thank you for helping me see that mark, However when I tried checking your equation it didn't seem to work. I think the difference is "C-" rather than "+C" I'm unsure how but that seems to be the only conversion difference, thank you too for your assistance
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