SOLUTION: justify y=x^2 using finite differences?

Question 1018384: justify y=x^2 using finite differences?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
write out the following sequence
1 4 9 16 25
calculate the difference between the terms
3 5 7 9
calculate the difference between the new terms
2 2 2
On the second line, the differences are all the same, the method of finite differences tells us that the polynomial generating this sequence is of order 2
:
the general form is f(x) = ax^2 +bx +c
:
let's look at f(1), f(2), f(3)
f(1) = a + b + c = 1
f(2) = 4a + 2b + c = 4
f(3) = 9a + 3b + c = 9
:
solving for a, b , c we see that a=1, b=0, c=0, therefore
:
f(x) = x^2 is our solution
:
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