WEBVTT
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Which of the following is the graph of a polynomial of even degree with a positive leading coefficient?
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Here, we have four different polynomials that all exhibit different characteristics.
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To solve the question, weβll need to remember what the characteristics of an even degree polynomial with a leading coefficient is.
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In an even degree polynomial, as π₯ approaches both positive and negative β, thatβs the π₯-values in both the directions, you have two possible options.
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The output will either be both sets of π¦-values approaching negative β or both sets of π¦-values approaching positive β.
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That means that the π¦-values are pointing in the same direction on either side.
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We see that, here, the π¦-values approach negative β and here as the π¦-values approach positive β.
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On the red graph, one side is approaching positive β and the other side negative β.
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And that means that answer choice a, the red graph, is an odd degree polynomial.
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And the same is true for the purple.
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It is also an odd degree polynomial.
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So how do we take b and c, the yellow and green graph, and determine which of them has a positive leading coefficient.
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Theyβre both even.
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But one is positive.
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And one is negative.
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As π of π₯ approaches plus or minus β with a positive leading coefficient, the π¦-values will be positive.
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Only the green graph have the π¦-values approaching positive β.
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The yellow graph would be an even degree polynomial with a negative leading coefficient.
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The green graph, answer choice c, is the only graph of an even degree polynomial with a positive leading coefficient.