Notes Over 6.9Writing a Cubic FunctionWriting a Cubic Function

.1

axf 4x

Write the cubic function whose graph is shown.Write the cubic function whose graph is shown.

0,4

0,2

0,1

8,0

2x 1x0 0 0 8

a88 88

1a

124 xxxxf

Notes Over 6.9Writing a Cubic FunctionWriting a Cubic Function

.2

axf 2x

Write the cubic function whose graph is shown.Write the cubic function whose graph is shown.

0,2

0,1 0,5

8,3

1x 5x3 8

a168 1616

2

1a

5122

1 xxxxf

3 31 2 8

Notes Over 6.9Finding Finite DifferencesFinding Finite Differences

54 .3 2 xxxf 1f

Show that the Show that the nnth-order differences for the given function of th-order differences for the given function of degree degree nn are nonzero and constant. are nonzero and constant.

2f 3f 4f 5f 6f8 19 38 65 100 143

11 19 27 35 438 8 8 8

The second-order differences are non-zero and constant.

Notes Over 6.9Finding Finite DifferencesFinding Finite Differences

3 .4 23 xxxf 1f

Show that the Show that the nnth-order differences for the given function of th-order differences for the given function of degree degree nn are nonzero and constant. are nonzero and constant.

2f 3f 4f 5f 6f1 9 33 77 147 249

10 24 44 70 10214 20 26 32

The third-order differences are non-zero and constant.

6 6 6

Notes Over 6.9Modeling with Cubic RegressionModeling with Cubic Regression

452 xxxf

Use a graphing calculator to find a polynomial function that Use a graphing calculator to find a polynomial function that fits the data.fits the data.

x 1 2 3 4 5 6

f(x) 8 10 10 8 4 -2

1a 5b 4cQuadratic

.5

Notes Over 6.9Modeling with Cubic RegressionModeling with Cubic Regression

112 23 xxxf

Use a graphing calculator to find a polynomial function that Use a graphing calculator to find a polynomial function that fits the data.fits the data.

x 1 2 3 4 5 6

f(x) -12 -11 -2 21 64 133

1a 2b 0cCubic

11d

.6

Notes Over 6.9