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Math Help - Finding the equation of a parabola from given information.

  1. #1
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    Finding the equation of a parabola from given information.

    Hi all, any help with this problem would be much appreciated.
    I have to find a quadratic equation, and am given this information.
    points (2,11) and (-1 and 2) lie on the graph.
    x=2 when gradient =6.
    I know this involves simultanous equations to find a, b and c, however i don't know what equations I have to use!
    Thanks for any help anyone could provide!!!!!
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  2. #2
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    Quote Originally Posted by dominicc View Post
    Hi all, any help with this problem would be much appreciated.
    I have to find a quadratic equation, and am given this information.
    points (2,11) and (-1 and 2) lie on the graph.
    x=2 when gradient =6.
    I know this involves simultanous equations to find a, b and c, however i don't know what equations I have to use!
    Thanks for any help anyone could provide!!!!!
    f(x) = a^2 + bx + c.

    f(2) = 11 and f(-1) = 2. Furtherfore f'(2) = 6. Write down the equations corresponding to these three conditions and solve them for a, b and c.
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  3. #3
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    By 'f'(2) = 6', does this mean 4a+b=6, or am I wrong with this?
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  4. #4
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    If f(x)= ax^2+ bx+ c, then f '(x)= 2ax+ b so f '(2)= 2a(2)+ b= 4a+ b= b. Yes, you are correct. You have three equations to solve for a, b, and c.
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