Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 353: 69

$f(x)=(x+3)^2(x-3)^2$

Step 1. Identify zeros from the graph: $x=-3,-3,3,3$ Step 2. Write a form of the polynomial: $f(x)=k(x+3)^2(x-3)^2$ where $k$ is unknown. Step 3. As point $(0,81)$ is on the curve, we have $f(0)=k(0+3)^2(0-3)^2=81$, thus $k=1$ Step 4. $f(x)=(x+3)^2(x-3)^2$