Functions from tables (using finite differences)

Function f

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) \(f(x)\)
1 2
2 6
3 12
4 20
5
100

Function g

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) \(g(x)\)
0 0
1 5
2 12
3 21
4 32
137

Function h

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) \(h(x)\)
1 -4
3 1
5 12
7 29
9 52
11 81
141

Function j

Give a linear function that would result in the values given below.

\(x\) \(j(x)\)
3 25
4 23
5 21
6 19
7 17
8 15

Function k

Unfortunately this method will not always work. Why won't it work in the example below?

\(x\) \(k(x)\)
0 1
1 2
2 4
3 8
4 16
5 32

Challenge: Function m

Give a polynomial function that would result in the values given below. Compute the missing value.

\(x\) \(m(x)\)
0 2
1 3
2 6
3 12
4 22
100

Random quadratic functions

x p(x)
1 1
2 2
3 4
4 7
5 11
100 4951

Coefficient answers for general quadratic: a = 1/2, b = -1/2, c = 1