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f(n)=(first difference)n+ y-intercept
ex. f(n)=2n+4

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____
0 | 4
1 | 6
2 | 8
3 | 10
4 | 12

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You know that a function is linear because the 1st difference is constant

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f(n)=f(n-1)+(first difference)
ex. f(n)=f(n-1)+2
DO NOT FORGET THE STARTING POINT!!
y-intercept
ex. f(1)=6 or f(0)=4

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You know a function is exponential because it has a common ratio

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____
1 | 2
2 | 4
3 | 8
4 | 16
5 | 32

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f(n)=f(n-1)x(common ratio)
ex. f(n)=f(n-1)x2
DO NOT FORGET THE STARTING POINT!!
y-intercept
ex. f(1)=2

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f(n)=(starting output)(common ratio)^n-1
ex. f(n)=2(2)^n-1

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You know a function is quadratic because the 2nd difference is constant

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____
1 | 3
2 | 12
3 | 27
4 | 48
5 | 75

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f(n)=f(n-1)+(2nd difference)+(y-intercept of the 1st difference)
ex. f(n)=f(n-1)+6n-3
DO NOT FORGET THE STARTING POINT!!
y-intercept
ex. f(0)=0

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f(n)=1/2(2nd difference)^2+differnce

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- Goes over how to write the recursive equation
- Explains how to get the second # in a recursive equation

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How to write quadratic recursive equations.

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- Goes over how to write the explicit equation
- Shows a different method other then the perfect square method of finding the first #

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Explicit Equations for Quadratic Functions

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Explicit Equations for Quadratic Functions