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Determine whether the given table of values represents a quadratic function x= -1 / 0 /1 / 2 / 3

y= 4 / 3 / 4 / 7 / 12

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2 answers

  1. starting at x=0, the 2nd differences are constant (2) so yes, it is a quadratic
    y = x^2+3

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  2. The difference between x-values ​​is constant so use differences of y- values to determine the model.

    If the second difference is the same value, the model will be quadratic.

    First difference of y-values:

    3 - 4 = - 1

    4 - 3 = 1

    7 - 4 = 3

    12 - 7 = 5

    Second difference of y-values:

    1 - ( - 1 ) = 1 + 1 = 2

    3 - 1 = 2

    5 - 3 = 2

    The second difference is the same value, so the given table of values represents a quadratic function.

    By the way this quadratic function is:

    y = x^2 + 3

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