Chapter 11.8, Problem 55SR

To determine

the model which fits the above data

Answer to Problem 55SR

The table of values represents a quadratic function.

Explanation of Solution

Given:

x	-3	-2	-1	0	1
y	14	9	6	5	6

Calculation:

The table of values is as follows.

x	-3	-2	-1	0	1
y	14	9	6	5	6

The objective is to determine the model which fits the above data. And then write the equation for the function that models the data.

At first find the differences of the data of the $y$ values.

So,

  $\begin{array}{l}9-14=-5\\ 6-9=-3\\ 5-6=-1\\ 6-5=1\end{array}$

Since, the first differences are not all equal. So, the table of values does not represent a linear function.

Now find the second differences of the data and compare.

So,

  $\begin{array}{l}-3-\left(-5\right)=2\hfill \\ -1-\left(-3\right)=2\hfill \\ 1-\left(-1\right)=2\hfill \end{array}$

The second differences are all equal. So, the table of values represents a quadratic function.

Conclusion:

The table of values represents a quadratic function.