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Math Help - Finding equation for quad function with given 3 points

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    Finding equation for quad function with given 3 points

    Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

    I have many problems similar to this but I don't know how to set it up. Help would be great =]
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    Quote Originally Posted by Kitty216 View Post
    Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

    I have many problems similar to this but I don't know how to set it up. Help would be great =]
    All quadratics can be written in the form

    y = ax^2 + bx + c.

    By substituting the three points, you end up with three equations in three unknowns that you can solve simultaneously.

    3 = a(-6)^2 + b(-6) + c

    -32 = a(1)^2 + b(1) + c

    3 = a(-4)^2 + b(-4) + c
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    Quote Originally Posted by Kitty216 View Post
    Find an equation for the quadratic function whose graph contains the points (-6,3), (1,-32), and (-4,3).

    I have many problems similar to this but I don't know how to set it up. Help would be great =]
    y = ax^2 + bx + c


    3 = a(-6)^2 + b(-6) + c

    -32 = a(1)^2 + b(1) + c

    3 = a(-4)^2 + b(-4) + c


    solve the system for the coefficients a, b, and c.
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    oh I see. Thanks guys!!

    Out of curiosity, what form of equation would be used if the 3 points were on a circle?
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    Quote Originally Posted by Kitty216 View Post
    oh I see. Thanks guys!!

    Out of curiosity, what form of equation would be used if the 3 points were on a circle?
    Then it would be

    (x - h)^2 + (y - k)^2 = r^2

    where (h, k) is the co-ordinate of the centre and r is the radius.

    If you have three points, once again you will get three equations in three unknowns.
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    oh ok! Thank you for the help!
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