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16 March, 13:57

Find the quadratic function f (1) = - 7 f (3) = - 19 and f (3) = - 49

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  1. 16 March, 14:13
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    Since problem says the function is quadratic, it must be a function, except that there is a typo: one of the f (3) must read f (-3).

    Assuming the last f (3) should read f (-3), then the data now read:

    f (1) = - 7 f (3) = - 19 and f (-3) = - 49

    The general quadratic is

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

    f (1) = - 7 = > a+b+c=-7 ... (1)

    f (3) = - 19 = > 9a+3b+c=-19 ... (2)

    f (-3) = - 49 = > 9a-3b+c=-49 ... (3)

    (2) - (3)

    6b=30 = > b=5

    (2) - (1)

    8a+2b=-12 = > 8a+10=-12 = > a = (-22/8) = - 2.75

    substitute a and b in (1)

    -2.75+5+c=-7 = > c=-9.25

    => quadratic is

    -2.75x^2+5x-9.25=0 for f (1) = - 7 f (3) = - 19 and f (-3) = - 49

    If the typo is not as assumed above, proceed similarly to get

    f (x) = - 4x^2-5x+2 for f (1) = - 7 f (-3) = - 19 and f (3) = - 49
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