Question

Given the graph of a polynomial function, determine the minimum possible degree, the zeros and if the multiplicity of the zeros is even or odd. Assume the end behavior and all turning points are represented on the graph. a. Determine the minimum degree of the polynomial based on the number of turning points. b. Approximate the real zeros of the function, and determine if their multiplicity is odd or even. a. Minimum degree 4 b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity) a. Minimum degree 3 b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity) a. Minimum degree 4 b. -4 (even multiplicity), -1 (even multiplicity), 3 (odd multiplicity) a. Minimum degree 3 b. -4, -1, and 3 (each with odd multiplicity)

          Given the graph of a polynomial function, determine the minimum possible degree, the zeros and if the multiplicity of the zeros is even or odd. Assume the end behavior and all turning points are represented on the graph.
a. Determine the minimum degree of the polynomial based on the number of turning points.
b. Approximate the real zeros of the function, and determine if their multiplicity is odd or even.
a. Minimum degree 4
b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity)
a. Minimum degree 3
b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity)
a. Minimum degree 4
b. -4 (even multiplicity), -1 (even multiplicity), 3 (odd multiplicity)
a. Minimum degree 3
b. -4, -1, and 3 (each with odd multiplicity)

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Given the graph of a polynomial function, determine the minimum possible degree, the zeros and if the multiplicity of the zeros is even or odd. Assume the end behavior and all turning points are represented on the graph.
a. Determine the minimum degree of the polynomial based on the number of turning points.
b. Approximate the real zeros of the function, and determine if their multiplicity is odd or even.
a. Minimum degree 4
b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity)
a. Minimum degree 3
b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity)
a. Minimum degree 4
b. -4 (even multiplicity), -1 (even multiplicity), 3 (odd multiplicity)
a. Minimum degree 3
b. -4, -1, and 3 (each with odd multiplicity)

Added by Nerea C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Caden Burrell

04/15/2022

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Since there are three turning points on the graph, the minimum degree of the polynomial is 4 (number of turning points + 1). Show more…

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Given the graph of a polynomial function, determine the minimum possible degree, the zeros and if the multiplicity of the zeros is even or odd. Assume the end behavior and all turning points are represented on the graph. a. Determine the minimum degree of the polynomial based on the number of turning points. b. Approximate the real zeros of the function, and determine if their multiplicity is odd or even. a. Minimum degree 4 b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity) a. Minimum degree 3 b. -4 (odd multiplicity), -1 (odd multiplicity), 3 (even multiplicity) a. Minimum degree 4 b. -4 (even multiplicity), -1 (even multiplicity), 3 (odd multiplicity) a. Minimum degree 3 b. -4, -1, and 3 (each with odd multiplicity)

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Transcript

00:01 So in this problem, we are given the graph of a polynomial function, and i am a asked to determine the minimum possible degree of the polynomial based on the number of turning points.

00:13 And then i'm asked part b to approximate the real zeros of the function and determine if their multiplicity is odd or even.

00:20 So first i want to determine the minimum degree of the polynomial based on the number of turning points.

00:25 So on this graph, i have one, two, three, three.

00:30 Turning points or three point on this graph in which the graph turns or changes direction.

00:36 The minimum degree of this polynomial is going to be one more than the total number of turning points.

00:43 So the number of turning points plus one, okay, which in this case, that means the minimum degree of this polynomial is four.

00:54 So a fourth degree polynomial is the smallest degree that this polynomial could be.

01:00 Okay.

01:01 So, part b wants me to approximate the real zeros of the function and determine if their multiplicity is odd or even.

01:07 So when it talks about real zeros of the function, when i'm looking for zeros, i'm looking for x intercepts.

01:14 So everywhere that y is equal to zero, or in other words, every time i cross the x axis, those are my zeros.

01:21 Or sometimes you'll hear them called solutions.

01:23 Okay...

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