Explain how to sketch a graph of the function f(x)=x^3+2x^2-8x. include end behavior, zeros, and intervals where the function is positive and negative

Step-by-step explanation:

f(x) = x³ + 2x² − 8x

To find the end behavior, take the limit as x approaches ±∞.  Since the leading coefficient is positive, and the order is odd:

lim(x→-∞) f(x) = -∞

lim(x→∞) f(x) = ∞

Next, factor to find the zeros.

f(x) = x (x² + 2x − 8)

f(x) = x (x + 4) (x − 2)

The zeros are (-4, 0), (0, 0), and (2, 0).

Therefore, the intervals are:

x < -4, f(x) < 0

-4 < x < 0, f(x) > 0

0 < x < 2, f(x) < 0

x > 2, f(x) > 0

step-by-step explanation: