Chapter 4 - Exponential and Logarithmic Functions - Section 4.9 Building Exponential, Logarithmic, and Logistic Models from Data - 4.9 Assess Your Understanding - Page 367: 15

$f(x)=\frac{1}{3}(x+3)(x-2)(x+1)^2$

1. There are three turning points, thus it is possible that the order is 4. 2. Identify zeros $x=-3,2$ (multiplicity 1) and $x=-1$ (multiplicity 2). 3. Write a possible form $f(x)=a(x+3)(x-2)(x+1)^2$ 4. Use point $(0,-2)$ to get $a(3)(-2)(1)=-2$ and $a=\frac{1}{3}$ 5. Thus $f(x)=\frac{1}{3}(x+3)(x-2)(x+1)^2$