Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) \[ f(x)=(x-3)^{2}+6 \] domain range

**Step 1: Domain** The function is \[ f(x)=(x-3)^2+6. \] Since this is a quadratic function (with a squared term) and there are no restrictions such as division by zero or a square root of a negative number, the function is defined for all real values of \( x \). Thus, the **domain** is: \[ (-\infty, \infty) \] **Step 2: Range** A quadratic function in the form \[ f(x)=(x-h)^2+k \] has its vertex at \((h,k)\). The given function has \( h = 3 \) and \( k = 6 \). Since the coefficient of the squared term is positive (implicitly \( 1 \)), the parabola opens upward. The vertex \((3,6)\) represents the minimum point of the function. Therefore, the smallest value \( f(x) \) can take is \( 6 \), and as \( x \) moves away from \( 3 \), \( f(x) \) increases without bound. Thus, the **range** is: \[ [6, \infty) \]