To find the vertical asymptote of the function \( y = 3 + \frac{12}{x - 5} \), we need to identify where the function is undefined.
The expression \( \frac{12}{x - 5} \) is undefined when the denominator equals zero. Thus, we set the denominator to zero and solve for \( x \):
\[ x - 5 = 0 \] \[ x = 5 \]
Therefore, there is a vertical asymptote at \( x = 5 \).
In conclusion, the vertical asymptote of the graph \( y = 3 + \frac{12}{x - 5} \) is \( x = 5 \).