7
QuizMultiple Choice

Graphing Polynomial Functions — Quiz

Question 7 • Mathematics III

Which statement describes the graph of f of x is equal to negative x to the 4th power plus 3 x cubed plus 10 x squared ?

Answer
A
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to negative 5 and x is equal to 2 .
B
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to negative 5 and x is equal to 2 .
C
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to 5 and x is equal to negative 2 .
D
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to 5 and x is equal to negative 2 .

Explanation

Factor the polynomial: f(x) = −x²(x − 5)(x + 2). The root x = 0 has multiplicity 2, so the graph touches the x-axis there; the roots x = 5 and x = −2 have multiplicity 1, so the graph crosses at both.

AI-written and checked against the verified answer.

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