12/3 Key Features of Polynomials

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What is a polynomial?

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What are the key features of a polynomial function?

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Key features include: degree, leading coefficient, zeros (roots), extrema (maxima and minima), and intervals of increase and decrease.

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How do you determine the degree of a polynomial?

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What does the leading coefficient of a polynomial indicate?

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The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial graph.

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What is the significance of the zeros of a polynomial?

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The zeros (or roots) of a polynomial are the values of x for which the polynomial equals zero. They represent the x-intercepts of the graph.

Tags

CCSS.HSF-IF.C.7C

Front

How can you identify the number of extrema in a polynomial graph?

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The number of extrema (maxima and minima) can be determined by analyzing the first derivative of the polynomial. The critical points where the derivative equals zero indicate potential extrema.

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What does it mean if a polynomial has an odd degree?

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If a polynomial has an odd degree, its graph will have opposite end behaviors: as x approaches positive infinity, y approaches positive or negative infinity, and as x approaches negative infinity, y approaches the opposite.

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What is the difference between increasing and decreasing intervals in a polynomial function?

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Increasing intervals are where the function's value rises as x increases, while decreasing intervals are where the function's value falls as x increases.

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What is a non-polynomial function?

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Front

How do you find the leading coefficient from a polynomial expression?

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