Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 186: 116

$f(x)=-2(x+4)(x+1)(x-2)$

Step 1. Given zeros $x=-4,-1,2$, we can write a general form of the function as $f(x)=a(x+4)(x+1)(x-2)$ where $a$ is unknown. Step 2. With y-intercept $(0,16)$, we have $f(0)=a(0+4)(0+1)(0-2)=16$, thus $a=-2$ Step 3. Thus the function is $f(x)=-2(x+4)(x+1)(x-2)$