Question

Help! Please! As soon as possible. Use finite differences to identify the degree of the polynomial that best describes the data:

Answer 1

quartic

Explanation:

The x-values increase by a constant 1. Find the differences of the y-values.

x 9 10 11 12 13 14

y −5 −8 −7 −4 1 10

−3 1 3 5 9 First differences

The first differences are not constant. Find the second differences.

x 9 10 11 12 13 14

y −5 −8 −7 −4 1 10

−3 1 3 5 9 First differences

4 2 2 4 Second differences

The second differences are not constant. Find the third differences.

x 9 10 11 12 13 14

y −5 −8 −7 −4 1 10

−3 1 3 5 9 First differences

4 2 2 4 Second differences

−2 0 2 Third differences

The third differences are not constant. Find the fourth differences.

x 9 10 11 12 13 14

y −5 −8 −7 −4 1 10

−3 1 3 5 9 First differences

4 2 2 4 Second differences

−2 0 2 Third differences

2 2 Fourth differences

The fourth differences are constant. Therefore, the data is quartic.

Answer 2

Analyze picture

most likely,

quintic