$\"\"$

\

Observe the table:

\

The ordered pair are $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Since, the second differences are all equal,

\

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

\

$\"\"$

\

write an equation for the function:

\

The equation has the form $\"\"$ .

\

Find the value of $\"\"$ .

\

Use the ordered pair is $\"\"$ .

\

$\"\"$ (Quadratic equation)

\

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

\

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

\

$\"\"$ (Multiply)

\

Write an equation.

\

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

\

$\"\"$ (Simplify)

\

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

\

$\"\"$

\

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