Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.
\[
f(x)=3 x^{2}+18 x-1
\]
Does the quadratic function $\mathrm{f}$ have a minimum value or a maximum value?
The function $f$ has a minimum value.
The function $\mathrm{f}$ has a maximum value.
What is this minimum or maximum value?
(Simplify your answer.)

Step 1 ：The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\).

Step 2 ：The coefficient of \(x^2\) is positive, so the parabola opens upwards. This means that the function has a minimum value.

Step 3 ：The minimum or maximum value of a quadratic function \(f(x) = ax^2 + bx + c\) is given by \(f(-\frac{b}{2a})\).

Step 4 ：So, we need to substitute \(x = -\frac{b}{2a}\) into the function to find the minimum value.

Step 5 ：Given that \(a = 3\), \(b = 18\), and \(c = -1\), we find that \(x = -3.0\).

Step 6 ：Substituting \(x = -3.0\) into the function, we find that the minimum value is \(-28.0\).

Step 7 ：Final Answer: The minimum value of the function is \(\boxed{-28}\).