Find quadratic functions for this problem?

Question

for this table

n: | 1 | 2 | 3 | 4 | 5 | ...

f(n): | 1 | 3 | 6 | 10 | 15 |...

if n = 1, then f(n) = 1; n=2 then f(n)=3; if n = 5 then f(n)=15; etc.

how would you write a quadratic function for that? please explain

thanks

Answer 1

Lets look here.

A quadratic has the form: ax^2+bx+c

Lets take a few of those and see what is possible.

a(1)^2+b*1+c=a+b+c=1

a(2)^2+b*2+c=4a+2b+c=3

a(3)^2+b*3+c=9a+3b+c=6

Now we have a system of three equations with three unknowns.

If you know how to solve that, then you are done. Otherwise somebody else will be along to explain that part.

The solution in this case if f(n)=1/2*n^2+1/2*n. (a=1/2, b=1/2, c=0)