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Math Help - Quadratic Equation from Coordinates?

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    Quadratic Equation from Coordinates?

    Hi guys, is there any way of figuring out an equation just using coordinates?
    for example if you had the points: (32, 6), (48, 9) and (96, 18)
    is there any way of manipulating those coordinates to form an accurate equation? (without trying to form a line of best fit and then using trial and error to get it as close as possible?)


    thanks.
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  2. #2
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    Quote Originally Posted by alex212121 View Post
    Hi guys, is there any way of figuring out an equation just using coordinates?
    for example if you had the points: (32, 6), (48, 9) and (96, 18)
    is there any way of manipulating those coordinates to form an accurate equation? (without trying to form a line of best fit and then using trial and error to get it as close as possible?)


    thanks.
    Yes. Recall that a general quadratic is of the form

    y = ax^2 + bx + c.


    Using the three points, you get

    6 = a(32)^2 + b(32) + c

    9 = a(48)^2 + b(48) + c

    18 = a(96)^2 + b(96) + c.


    Simplify each equation, then solve the three equations simultaneously for a, b, c.
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