When you're graphing (or looking at a graph of) polynomials, it can help to already have an idea of what basic polynomial shapes look like. One of the aspects of this is "end behavior", and it's pretty easy. We'll look at some graphs, to find similarities and differences.
First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:
In 2x^3 - 7x^2 - 7x + 12, The leading coefficient is 2, and its a Posituve number
If the degree of a polynomial f(x) is even and the leading coefficient is positive, then f(x) → ∞ as x → ±∞. ... If f(x) is an odd degree polynomial with positive leading coefficient, then f(x) →-∞ as x →-∞ and f(x) →∞ as x → ∞.