Question

A.Sketch the graph of the following polynomial functions.

1.f(x)= (x+2)(x-1)(x-2)
2.f(x)=-x(x+1)(2x-3)
3.f(x)=x(x+3)(x+1)(x-2)

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Answer 1

Answer:

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Answer 2

Answer:

The x-intercept x=−3 is the solution to the equation (x+3)=0. The graph passes directly through the x-intercept at x=−3. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.

The x-intercept x=2 is the repeated solution to the equation (x−2)2=0. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.

Step-by-step explanation:

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