$\"\"$

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Observe the table:

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The ordered pair are $\"\"$ .

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Find the first differences of $\"\"$ -values in the ordered pair.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Since the first differences are not all equal .

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Hence the table of values does not represent a linear function.

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Find the second difference of $\"\"$ -values in the ordered pair.

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$\"\"$

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$\"\"$

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$\"\"$

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Since, the second differences are all equal,

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Therefore, the table of values are represent a quadratic function.

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$\"\"$

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write an equation for the function:

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The equation for quadratic function is $\"\"$ .

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Find the value of $\"\"$ .

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Use the ordered pair $\"\"$ .

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$\"\"$ (Quadratic equation)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Substitute $\"\"$ in the formula)

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$\"\"$ (Multiply)

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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Write an equation.

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$\"\"$ (Substitute $\"\"$ in the formula)

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$\"\"$ (Simplify)

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An equation that models the data is $\"\"$ .

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$\"\"$

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The table of values represents a quadratic function $\"\"$ .