Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 209: 70

$y=-\frac{1}{4}(x+1)^2(x-1)(x-4)$.

Step 1. Find zeros $x=1,4$ (multiplicity 1), $x=-1$ (multiplicity 2). Step 2. Write a general form $y=a(x+1)^2(x-1)(x-4)$. Step 3. Use point $(3,8)$, $8=a(3+1)^2(3-1)(3-4)$, we have $a=-\frac{1}{4}$ Step 4. Provide the answer $y=-\frac{1}{4}(x+1)^2(x-1)(x-4)$.