Final answer:
The domain of the function is found by solving the equation 6x^2-3x-10=0. Vertical asymptotes can be identified by finding the values of x that make the denominator equal to zero.
Step-by-step explanation:
The domain of the function f(x) = (x-3)^2/(6x^2-3x-10) consists of all real numbers except for values that make the denominator equal to zero. To find the domain, we need to solve the equation 6x^2-3x-10=0. We can do this by factoring or using the quadratic formula. After finding the domain, we can determine the vertical asymptotes by identifying the values of x that make the denominator equal to zero. These values indicate where the graph approaches infinity or negative infinity.