# Video: Identifying the Degree of a Polynomial Function from its Graph

The given graph is of a polynomial đť‘“. What is the degree of đť‘“? [A] 1 [B] 2 [C] 3 [D] 4 [E] 5

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### Video Transcript

The given graph is of a polynomial đť‘“. What is the degree of đť‘“? Is it one, two, three, four, or five?

Remember, a polynomial of degree or order đť‘› can have up to đť‘› minus one turning points. In other words, if we can find the degree of our polynomial, we can know it can have up to one less than this turning points. So, letâ€™s count the turning points of our graph. We see the graph changes direction here and here. But whatâ€™s happening over here? Well, the graph doesnâ€™t actually appear to fully change direction, and thatâ€™s because it doesnâ€™t. This is, in fact, a point of inflection. Itâ€™s a point where the concavity of the graph changes.

Now, another fact is that a polynomial of degree đť‘› can have up to đť‘› minus two inflection points. And we can think of the inflection points a little bit like the graph changing direction really quickly twice in a short space of time. We can consider this as two turning points. This means we have a total of four. And so, the degree of our polynomial must be five.