What is the behavior of the graph y=2x3+x2−7x−6 at each of its zeros

At the given zeros of the function (-1.5, -1, and 2), the graph will behave like a sine curve, cutting the x-axis at three points.

The given polynomial expression:

y = 2x³ + x² - 7x - 6

The zeros of a polynomial equation are the values of x at which the given function equals zero.

The first zero of the given function is at x = 2;

f(2) = 2(2)³  + (2)²  - 7(2)  - 6

     = 16   +  4  - 14  - 6

     = 20   -    20  =  0

The second zero of the given function is at x = -1;

f(-1)  = 2(-1)³  + (-1)²   - 7(-1)   -   6

      = -2    +   1   +   7   -  6

      = - 8  +  8 =  0

The third zero of the given function is at x = -1.5;

f(-1.5)  = 2(-1.5)³   +  (-1.5)²   -  7(-1.5)   -  6

          = - 6.75    +  2.25   + 10.5    -  6

          = - 12.75  + 12.75  = 0

The zeros of the given function include;

----(-1.5)-------(-1)------------------------------(2)--------

Therefore, at the given zeros of the function (-1.5, -1, and 2), the graph will behave like a sine curve, cutting the x-axis at three points.

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step-by-step explanation:

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