Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 209: 67

$y=-\frac{1}{2}(x+1)(x-1)^2(x-2)$

Step 1. Find zeros $x=-1,2$ (multiplicity 1), $x=1$ (multiplicity 2). Step 2. Write a general form $y=a(x+1)(x-1)^2(x-2), a\lt0$. Step 3. Use point $(0,1)$, $1=a(0+1)(0-1)^2(0-2)$, we have $a=-\frac{1}{2}$ Step 4. Provide the answer $y=-\frac{1}{2}(x+1)(x-1)^2(x-2)$