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How do I create a quadratic equation that passes through the points (-1,2),(1,7),(4,5)?

  • Math -

    y = a x ^ 2 + b x + c


    In this case:


    For x = - 1 , y = 2

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

    a - b + c = 2


    For x = 1 , y = 7

    7 = a ( 1 ) ^ 2 + b 1 + c

    a + b + c = 7


    For x = 4 , y = 5

    5 = a ( 4 ) ^ 2 + b 4 + c

    16 a + 4 b + c = 5


    So you must solve system of 3 equations :

    a - b + c = 2

    a + b + c = 7

    16 a + 4 b + c = 5


    The exact solutions are :

    a = - 19 / 30

    b = 5 / 2

    and

    c = 77 / 15


    y = ( - 19 / 30 ) x ^ 2 + ( 5 / 2 )x + 77 / 15

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