$\"\"$

Observe the table:

The ordered pair are $\"\"$ .

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

$\"\"$

Since the first differences are not all equal.

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

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

$\"\"$

Since, the second differences are all equal,

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

$\"\"$

The table of values are represents a quadratic function.