Suppose somebody writes down an equation for a 5th-degree polynomial function in standard form and tells you that it has only one real zero (but not where it is). They tell you that you are allowed to ask any two questions about the polynomial, and once those two questions have been answered, you should try to graph the polynomial.
What two questions would you ask, and why?
In your answer, state what your two questions would be, and describe how you would use the information given to graph the function. You may want to make up an example of your own to show how the information you ask for would be useful to you. You might also want to consider whether there are any cases in which your strategy would fail.