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I've got stuck on the question asking, "Estimate the coordinates of each turning point and state whether each corresponds to a local maximum or a local minimum. Then estimate all real zeros and determine the least degree the function can have."

The question provided the graph as following, The provided graph.

Anyhow, I've got the local min&max and zeros.

Local MIN (2,-2)

Local MAX (1,0) & (3,0)

Zero {1,3}

However, I've got confused and stuck at getting least degree. Slader said the right answer was 4th degree because it intersect x-axis 4 times which I don't get.

Anyhow, I appreciate your help. Please make it highschoolish as possible. Thanks.

(I tried searching but everything was too advanced.)

1 Answers 1

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While circumventing calculus (it can kill the problem), here's what we can say: the minimal degree of a polynomial given its graph is the number of turning points plus one. It's just how things are. You can't quite count the number of roots because of multiplicity - this means roots may repeat.

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    Multiplicity would only increase the degree. You can always say that if it crosses the axis four times then the degree is at the very least $4$. – 2017-02-06