Determine the vertex of the parabola without graphing. \[ f(x)=3 x^{2}-18 x+25 \] What is the vertex of the parabola? (Type an ordered pair.)

Step 1 ：The vertex of a parabola given in the form \(f(x) = ax^2 + bx + c\) is at the point \((-b/2a, f(-b/2a))\). In this case, \(a = 3\), \(b = -18\), and \(c = 25\).

Step 2 ：So, the x-coordinate of the vertex is \(-(-18)/(2*3) = 3\).

Step 3 ：We can substitute \(x = 3\) into the equation to find the y-coordinate of the vertex.

Step 4 ：The vertex of the parabola is \(\boxed{(3, -2)}\).