Question

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

How do I solve this?

Answer 1

if the polynomial is of degree 2 then write

ax^2 + bx + c

then write a(x +1)^2 + b(x+1) + c - (ax^2 + bx + c) = 6x - 8
since this corresponds to f(x+1) - f(x)

then do a(1)^2 + b(1) + c = 26
since this corresponds to f(1)

hopefully this reduces to a manageable system of equations that you can find the general equation quite easily with

Answer 2

or you can just put x=1 in f(x+1) -f(x) = 6x-8
since you know f(1), you can find f(2), just by putting x=1 on both sides.

Answer 3

do what @hartnn suggested, will save you tons of work

Answer 4

so I will sub x for one on both sides. So it will be f(1+1)-f(1)=6(1)-8

Answer 5

yes! go on....

Answer 6

so will it work out to 2-1 = 6-8 ?????

i just get confused at this part because i don't know what to do

Answer 7

no remember it's f(2) - f(1) = 6(1) - 8

Answer 8

f(1+1) = f(2)
so, you have
f(2) - f(1) =6-8
and you know f(1) = 26
just plug in and find f(2)

Answer 9

??? could you explain it a different way...if you don't mind