Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 353: 70

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

Step 1. Identify zeros from the graph: $x=-1,-1,2$ Step 2. Write a form of the polynomial: $f(x)=k(x+1)^2(x-2)$ where $k$ is unknown. Step 3. As point $(0,4)$ is on the curve, we have $f(0)=k(0+1)^2(0-2)=4$, thus $k=-2$ Step 4. $f(x)=-2(x+1)^2(x-2)$