Jonathan F. answered • 03/11/16

Passionate About Algebra

"Extrema" is the plural; "extremum" is the singular. You have 1 extremum or 2+ extrema.

Suneet P.

asked • 08/22/15Hi 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!

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Jonathan F. answered • 03/11/16

Passionate About Algebra

"Extrema" is the plural; "extremum" is the singular. You have 1 extremum or 2+ extrema.

Michael J. answered • 08/22/15

Effective High School STEM Tutor & CUNY Math Peer Leader

Looking at the x-intercepts will not help much because of the multiplicity. By multiplicity, the x-intercepts appear more than once.

You can have x-intercepts of -1 , 2 , and 2. This does not mean the degree is 3. Yes, we have 3 x-intercepts, but we only have 2 distinct x-intercepts: -1 and 2.

Here is an example:

x^{2} + 2x + 1 = 0 -------> (x + 1)(x + 1) = 0

has x-intercepts of -1 and -1. This polynomial has a degree of 2, but there is only 1 distinct x-intercept. -1

The best way to determine the degree is to examine the variable's exponents of the quadratic equation's leading term.

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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08/22/15

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Suneet P.

08/22/15