Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 186: 117

$f(x)=-2(x+5)^2(x-2)(x-4)$

Step 1. Given zeros and multiplicities, we can write a general form of the function as $f(x)=a(x+5)^2(x-2)(x-4)$ where $a$ is unknown. Step 2. With known point $(3,128)$ on the curve, we have $f(3)=a(3+5)^2(3-2)(3-4)=128$, thus $a=-2$ Step 3. Thus the function is $f(x)=-2(x+5)^2(x-2)(x-4)$