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Chapter 9: Q61. (page 596)

Look for a pattern in each table of values to determine which kind of model best describes the data. Then write an equation for the function that models the data.

x

0

1

2

3

4

y

0

-1

-4

-9

-16

Short Answer

Expert verified

The equation of the function that models best the given data is y=鈭�x2.

Step by step solution

01

Step 1. Determine the first and second differences.

Find the first and second differences as required.

First difference:

Second difference:

02

Step 2. Write an equation for the functions that models the data. 

Since the second differences are equal, the table of values represents a quadratic function of the form y=ax2.

03

Step 3. Simplify the equation for the function.

To find a, use an ordered pair from the table, such as (2,鈭�4).

y=ax2鈭�4=a脳224a=鈭�4a=鈭�1y=鈭�x2

An equation that models the data is y=鈭�x2.

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