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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