$\"\"$

Observe the table:

The ordered pair are $\"\"$ .

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

The series of first differences: $\"\"$

$\"\"$

Therefore, the second differences are all equal.

So, the table of values represent a quadratic function.

$\"\"$

The table of values represents a quadratic function.