Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 186: 115

$f(x)=3(x+3)(x-1)(x-4)$

Step 1. Given zeros $x=-3,1,4$, we can write a general form of the function as $f(x)=a(x+3)(x-1)(x-4)$ where $a$ is unknown. Step 2. With y-intercept $(0,36)$, we have $f(0)=a(0+3)(0-1)(0-4)=36$, thus $a=3$ Step 3. Thus the function is $f(x)=3(x+3)(x-1)(x-4)$