Suneet P.

asked • 08/22/15

Polynomial Degree question

Hi guys I had a quick question? How do you determine the minimum degree of a function. Do you look at the roots or the extrema in the graph? If you do look at the x intercepts couldn't that answer be wrong since you are not accounting for imaginary roots.? Please help I have researched this topic everywhere and have been unable to find a clear and direct answer.THANK YOU!

2 Answers By Expert Tutors


Michael J. answered • 08/22/15

Effective High School STEM Tutor & CUNY Math Peer Leader

Suneet P.

Thanks! But i guess i should have been more specific. I was referring to a graph. For example what if there was a graph that crossed the x axis at 2 points and had 3 extrema.(sign changes from up to down or vice versa). Are you suppose to rely on the x intercepts or the the extrema


Michael J.

I would rely on the number of extremas (minimum and maximum).  Note a that polynomial of degree 1 has no extrema.  A polynomial of degree 2 has one extrema.  A polynomial of degree 3 has two extremas.   Following this pattern, we see that
The degree of any polynomial is the number of extremas minus 1.


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