Answer the questions below about the quadratic function.
\[
g(x)=-x^{2}+4 x-6
\]
Does the function have a minimum or maximum value?
Minimum
Maximum
Where does the minimum or maximum value occur?
\[
x=
\]
What is the function's minimum or maximum value?

Step 1 ：The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\), where \(a = -1\), \(b = 4\), and \(c = -6\).

Step 2 ：Since the coefficient of \(x^2\) (i.e., \(a\)) is negative, the parabola opens downwards. This means the function has a maximum value.

Step 3 ：The maximum or minimum value of a quadratic function \(f(x) = ax^2 + bx + c\) occurs at \(x = -b/(2a)\).

Step 4 ：The maximum or minimum value of the function is \(f(-b/(2a))\).

Step 5 ：Let's calculate these values.

Step 6 ：\(a = -1\), \(b = 4\), \(c = -6\)

Step 7 ：\(x_{vertex} = 2.0\)

Step 8 ：\(max_{value} = -2.0\)

Step 9 ：The x-coordinate of the vertex (where the maximum value occurs) is 2.0 and the maximum value of the function is -2.0. These are the answers to the questions.

Step 10 ：Final Answer: The function has a maximum value. The maximum value occurs at \(x = 2.0\). The maximum value of the function is \(\boxed{-2.0}\).