Answer
The y-intercept is 0
The x-intercepts are -2, 0, and 1
$\lim\limits_{x \to \infty} x^3(x+2)^2(x-1) = \infty$
$\lim\limits_{x \to -\infty} x^3(x+2)^2(x-1) = \infty$
Work Step by Step
$y = x^3(x+2)^2(x-1)$
When $x=0$, then $~~y = (0)^3(0+2)^2(0-1) = 0$
When $y=0$:
$x^3(x+2)^2(x-1) = 0$
$x = 0, -2,1$
$\lim\limits_{x \to \infty} x^3(x+2)^2(x-1) = \infty$
This limit is the product of a large magnitude positive number, a large magnitude positive number, and a large magnitude positive number.
$\lim\limits_{x \to -\infty} x^3(x+2)^2(x-1) = \infty$
This limit is the product of a large magnitude negative number, a large magnitude positive number, and a large magnitude negative number.
Note that the graph does not cross the x-axis at $x = -2$ because the term $(x+2)^2$ has an even exponent.
