Chapter 9.3, Problem 52E

To determine

To find: the polynomial function to model the set of data.

Answer to Problem 52E

  $-0.067x^2+0.73x-13.6$ .

Explanation of Solution

Given:

$x$	$-10$	$-7$	$-4$	$-1$	$2$	$5$	$8$	$11$	$14$
$y$	$-15$	$-9.2$	$-6.9$	$-3$	$-0.1$	$2$	$1.1$	$-2.3$	$-4.5$

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The tabular data of domain as $x$ and range $y$ while connecting the point to form curve which can be plot as graph using graphing calculator.

Calculation:

It needs to find a polynomial function to model the set of data:

$x$	$-10$	$-7$	$-4$	$-1$	$2$	$5$	$8$	$11$	$14$
$y$	$-15$	$-9.2$	$-6.9$	$-3$	$-0.1$	$2$	$1.1$	$-2.3$	$-4.5$

Use graph software to plot the data points $\left(x,f\left(x\right)\right)$ and select trendline option. The following is the graph of the polynomial whose expression is:

  $-0.067x^2+0.73x-13.6$ . Obtained from the graph software.

Hence, $-0.067x^2+0.73x-13.6$ .