Answers Summer_Advanced AlgebraGraphing Polynomial Functions

Graphing Polynomial Functions Answers

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At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?

–5

–2

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At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x-axis?

–7

–4

A polynomial function has a root of –5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?

The graph of the function is positive on (, –5).

The graph of the function is negative on (–5, 3).

The graph of the function is positive on (, 1).

The graph of the function is negative on (3, ).

Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.

The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.

A polynomial function has a root of –4 with multiplicity 4, a root of –1 with multiplicity 3, and a root of 5 with multiplicity 6. If the function has a positive leading coefficient and is of odd degree, which could be the graph of the function?

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