Answer
a. $x → ∞, P(x) → -∞$
$x → -∞, P(x) → ∞$
b. See graph below.
Work Step by Step
The question asks for the end behavior and a graph of P(x)
Given $P(x) = -(x-1)^2 (x-4)(x+2)^2$
The degree of P(x) is odd and the leading coefficient is negative.
Thus the end behavior will be:
$x → ∞, P(x) → -∞$
$x → -∞, P(x) → ∞$
See graph below.