Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities

Learn how to graph polynomial functions using end behavior, zeros, as well as multiplicities in this video math tutorial by Mario's Math Tutoring. We discuss how to find the zero through factoring and the zero product property. We also discuss whether the graph is going up or down to the right using the leading coefficient test and the degree of the polynomial. Lastly we discuss what the graph of the polynomial looks like when the multiplicity of the zeros is 1, 2, 3, or more. We go through 3 examples to illustrate this concept.
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Mario, you are so helpful, God will bless you forever. Please when the function is not in the factorized, what is the approach in graphing?

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[@xiaosongwu6744]

Great video, thanks! Suggestion: in 2nd polynomials, it was written “- x^x = 0” well, -1 is actually the leading coefficient, not part of the first factor/term. In the video, it went on by multiplying -1 on both sides of the equation to get to x^x = 0, which is completely unnecessary and quite confusing. We just need to recognize -1 being the leading coefficient, to avoid the confusion.

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Hi Do you have video for finding local max/min and global max/min?

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TI84 TI83 Finding Relative Maximum & Minimum
ua-cam.com/video/5zH9bPKrqO4/v-deo.html

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Please add this question too. Write an exact equation for this polynomial function using the additional point provided. Assume all zeros are integers.

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Can you give us non factored example? I'm struggling hard with graphing those. As an example, x^4 + 2x^2 -4

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Hey Mario, when you have a multiplicity of 3 why doesn’t it bounce off that point?

[@MariosMathTutoring]

Odd multiplicities go through, even multiplicities will ‘bounce’

[@livinlife123]

in the first example, what is the point of the two in the front?

[@MarleneBaugh]

The 2 infront is the leading coefficient which determines whether you go up or down to the right. If the leading coefficient is positive the graph goes up to the right. But if the leading coefficient is negative the graph goes down to the left eg. In a negative x Sq graph. The graph turns down. He this helps

[@RagerBlazer1]

what if it doesnt have a leading coefficient (the one with the paretheses)

[@MariosMathTutoring]

Do you mean like y=(x-1)^3 ? Then the leading coefficient is positive 1

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For the last problem the graph looks like a W

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