Chapter SH, Problem 9.29EP

To determine

To find: The function represented in the given data.

Answer to Problem 9.29EP

The given data represents a quadratic function.

Explanation of Solution

Given information:

The given data is shown below.

$x$	$-2$	$-1$	0	1	2
$y$	$-13$	$-6.25$	0	$5.75$	$11$

Calculation:

In the given table, the different value of $y$ is given for the different value of $x$ . So, the given data represents a function.

To find the relation, find the first differences of the values of $y$ .

  $\begin{array}{c}-6.25-\left(-13\right)=6.75\\ 0-\left(-6.25\right)=6.25\\ 5.75-0=5.75\\ 11-5.75=5.25\end{array}$

From the above differences, it is clear that the differences are not equal. So, find the second difference.

  $\begin{array}{c}6.25-6.75=-0.50\\ 5.75-6.25=-0.50\\ 5.25-5.75=-0.50\end{array}$

From the above differences, it is clear that the differences are equal. So, the given data represents a quadratic function.

Therefore, the given data represents a quadratic function.