To find the domain of the quadratic function \( y = x^2 - 12x + 36 \), we need to identify the values of \( x \) for which the function is defined.
Quadratic functions are defined for all real numbers, meaning there are no restrictions on the values of \( x \). Therefore, the domain of the function \( y = x^2 - 12x + 36 \) is:
\[ \text{Domain: } (-\infty, \infty) \]