Chapter 9, Problem 59SGR

To determine

Find the equation that describes best the data.

Answer to Problem 59SGR

The equation models best the given data is $y=3x^2$

Explanation of Solution

Given:

  

Concept Used:

First difference:

  

Second difference:

  

Since the second differences are equal, the table of values represents a quadratic function of the form $y=a{x}^2$ .

Calculation:

Since the second differences are equal, the table of values represents a quadratic function of the form $y=a{x}^2$ .

To find $a$ , use an ordered pair from the table, Such as (1, 3)

  $\begin{array}{l}y=a{x}^2\\ $ 3=a·{(1)}^2=a·1=a$a=3\end{array}$

An equation that models the data is $y=3x^2$

Thus, an equation that models the data is $y=3x^2$