Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 16

$$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{3/2}\right)^{2}=1. $$

Since the vertices are $(\pm 3,0)$ and the asymptotes are $y=\pm \frac{1}{2}x$, then we have $a=3, \frac{b}{a}=\frac{b}{3}=\frac{1}{2} $, and hence $b=\frac{3}{2} $. Hence, the equation of the hyperbola is given by $$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{3/2}\right)^{2}=1. $$