I have found an answer and I need help formulating the proof.
I have two equations, f(x)=(x+2)(x-(3+2i))(x-(3-2i)) and g(x)=-(x+2)(x-(3+2))(x-(3-2)) and then I have the straight line y=4x+8. I need to make a general statement and express g(x) in terms of f(x) and the straight line.
Any point on the straight line has the equal vertical distance to both curves. How can I express that mathematically?

Question

I have found an answer and I need help formulating the proof. 
I have two equations, f(x)=(x+2)(x-(3+2i))(x-(3-2i)) and g(x)=-(x+2)(x-(3+2))(x-(3-2)) and then I have the straight line y=4x+8. I need to make a general statement and express g(x) in terms of f(x) and the straight line. 
Any point on the straight line has the equal vertical distance to both curves. How can I express that mathematically?

anonymous · Answer

how about 
$$f(x)+g(x)=2(4x+8)$$?

anonymous · Answer

$$f(x)=x^3-4 x^2+x+26$$
$$g(x)=-x^3+4 x^2+7 x-10$$

anonymous · Answer

so 
$$f(x)+g(x)=8x+16$$

anonymous · Answer

perfect, exactly what i was looking for =) thank you.

anonymous · Answer

yw