I need help solving this problem f(x)=2x^2+1 find and simplify f(x+2)-f(x)/2?

2 Answers
Feb 2, 2017

f(x+2)-f(x)/2=x^2+8x+17/2

Explanation:

f(x) = 2x^2 + 1

f(x+2) - f(x)/2

First, find f(x+2) by plugging x+2 into the original equation

f(x+2) = 2(x+2)^2 + 1
f(x+2) = 2(x^2+4x+4) + 1
f(x+2) = 2x^2+8x+9

Next, find f(x)/2 by substituting 2x^2+1 for f(x)

f(x)/2 = (2x^2+1)/2
f(x)/2 = x^2+1/2

Combine your answers for the final answer by substitution

f(x+2) - f(x)/2
= (2x^2+8x+9) - (x^2+1/2)
=x^2+8x+17/2

Feb 2, 2017

x^2+8x+17/2

Explanation:

f(x+2)-f(x)/2
" "
=2(x+2)^2+1-(2x^2+1)/2
" "
=2(x^2+4x+4)+1-(2x^2)/2-1/2
" "
=2x^2+8x+8+1-x^2-1/2
" "
=2x^2-x^2+8x+8+1-1/2
" "
=x^2+8x+17/2