Find zeros and y intercept and describe the end behavior in proper notation. then sketch the graph. 3x^3+2x^2-12x-8

The zeros of the given equation are 2, -2 and -0.667. The y-intercept of the graph is f(0) = -8.

Explanation:

The given expression is,

To find zeros put f(x)=0

This equation is satisfied by x=2, so (x-2) is the factor of the given equation. By synthetic division or long division we can find the remaining factor.

Use Factoring method.

Equate each factor equal to zero by using zero product property.

So the zeros of the given equation are 2, -2 and -0.667.

To find the y-intercept of the graph, put x=0.

So the y-intercept of the graph is f(0) = -8.

Since the higher degree is 3 , which is odd and the coefficient of higher degree is positive, therefore the ead behavior is defined as,

It means as x decreases unboundedly then the function decreases unboundedly. similarly x increases unboundedly then the function increases unboundedly.

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step-by-step explanation: