Download Example 1→ Write the cubic function whose graph is shown

Name: ___________________________
Date: ________________ Block: _____
Ms. Gallagher
Example 1 Write the cubic function whose graph is shown.
Finite Differences
The differences between y – values given consecutive x - values
Example 2 Find the Finite Differences
a) f(–1) = -11
f(0) = -3
f(1) =1
f(2) = 1
f(3) = 3
b) f(–1) = -8
f(0) = -2
f(1) =4
f(2) = 10
f(3) = 16
c) f(–1) = -3
f(0) = -2
f(1) =-1
f(2) = 6
f(3) = 25
Properties of Finite Difference
If a polynomial function has a degree of n, then the nth – order differences
are nonzero and constant
If the nth – order differences are constant or zero, then the polynomial
function has a degree on n
Example 3Model the Finite Differences
The first seven triangular pyramidal numbers are shown below. Find a polynomial function
that gives the nth triangular pyramidal numbers.
You Try Use the calculator to find the model
The first five centered square numbers are shown below. Find the polynomial function that
gives the nth centered square number.