Chapter 9.7, Problem 23PPE

To determine

To calculate:

The set of data pairs that model with a quadratic function.

Answer to Problem 23PPE

The set of data pairs that could be modeled with a quadratic function is, $\left(1,7\right),\left(2,12\right),\left(3,19\right),\left(4,28\right),\left(5,39\right)$ .

Explanation of Solution

Calculation:

A set of data pairs that have second common difference constant and same for its $y-$ value is modeled by a quadratic function.

Hence, choose any set of data such that the $y-$ values show a constant second common difference.

So, the set is as follows:

$\left(x\right)$	$1$	$2$	$3$	$4$	$5$
$\left(y\right)$	$7$	$12$	$19$	$28$	$39$

Now, get the second common difference,

Day $\left(x\right)$	$1$	$2$	$3$	$4$	$5$
Visitors $\left(y\right)$	$7$	$12$	$19$	$28$	$39$
First Common Difference	---	$12-7=5$	$19-12=7$	$28-19=9$	$39-28=11$
Second Common Difference	---	---	$7-5=2$	$9-7=2$	$11-9=2$

Observe that the second common difference is same.

Hence the equation fits the data exactly.

Therefore, the set of data pairs that could be modeled with a quadratic function is,

  $\left(1,7\right),\left(2,12\right),\left(3,19\right),\left(4,28\right),\left(5,39\right)$ .