Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 353: 65

$f(x)=\frac{1}{2}(x+6)(x-2)(x-5)$

Step 1. Identify zeros from the graph: $x=-6,2,5$ Step 2. Write the form of the polynomial: $f(x)=k(x+6)(x-2)(x-5)$ where $k$ is unknown. Step 3. As point $(0,30)$ is on the curve, we have $f(0)=k(0+6)(0-2)(0-5)=30$, thus $k=\frac{1}{2}$ Step 4. $f(x)=\frac{1}{2}(x+6)(x-2)(x-5)$