A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.07x^2 + 40x − 105, and the cost of distributing by truck can be modeled as −0.03x^2 + 22x − 180, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

−0.04x^2 + 62x − 285
−0.1x^2 + 18x − 285
−0.04x^2 + 18x − 285
−0.04x^2 + 18x + 75

Question

A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.07x^2 + 40x − 105, and the cost of distributing by truck can be modeled as −0.03x^2 + 22x − 180, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

−0.04x^2 + 62x − 285
−0.1x^2 + 18x − 285
−0.04x^2 + 18x − 285
−0.04x^2 + 18x + 75

danjs · Answer

The difference would be the difference in value of the functions, say train is T(x) and truck is t(x)

The difference is 
T(x) - t(x)

danjs · Answer

Here is a graph of both functions, and their difference function

danjs · Answer

I just picked x=225 as a random value, notice how the green difference function is the difference of the two functions
5351.25 - 3251.25 = 2100`