Justifying Our Predictions for the Degree of a Polynomial Based on a Table
Comment on both the input values and the output values
e.g. "consecutive and equally spaced input values"
e.g. "output values have a constant second difference"
There is a difference between saying "the second differences are constant" and "the second differences are increasing by a constant amount."
Mention specific values related to the table. It should be clear that you looked at the table and didn't just write a "here's how you justify" sentence you memorized ahead of time. You can write your perfect sentence, but then add in proof you looked at the table.
On any assessment this semester, this justification will be either fill in the blank or multiple choice. Second semester you will have to write the sentence without any crutch.