given a polynomial f(x) of degree 2 where f(x+1)-f(x)=6x-8 and f(1)=26, then f(2) is?

Question

How to get 24 as the answer?

Answer 1

Well, I know that f(x+1)-f(x)=6x-8.

I have been given f(1)=26 so the x as been defined as one. Also, the value  of the function f(x+1) at 1 has the same value as the function f(x) at 2.

f(x+1)-f(1)=6x-8

f(x+1)-26=6x-8

f(x+1)=6x+18

 

The x has been defined as one. So we will evaluate f(x+1) at x=1. Of course, the value of f(x+1) at x=1 will be the same as the value of the function f(x) at 2 or f(2). 

 

plug in the x value of 1 to get to get the value of f(x+1) at one or the value of f(x) at x=2 

 

f(1+1)=6(1)+18=f(2)

f(1+1)=24=f(2)

f(2)=24