The key features of polynomials are the vertex, axis of symmetry, x and y intercepts.
1. The degree will help you find the end behavior.
2. The vertex shows you where it changes concavity.
3. X and y intercepts give you a couple of points of reference.
4. Axis of symmetry is only applicable to even degree polynomials.
I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.