The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. In the case of a quadratic function, the vertex is always of the form (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
The function g(x) = f(-x) - 2 can be obtained from the function f(x) by replacing all instances of x with -x and then subtracting 2 from the result. This transformation will flip the parabola over the y-axis and shift it down by 2 units.
The vertex of the parabola resulting from the function g(x) will be the point where the parabola reaches its highest or lowest point after this transformation. Since the parabola is flipped over the y-axis and shifted down by 2 units, the vertex of the resulting parabola will have the same x-coordinate as the original vertex (-6) and a y-coordinate that is 2 units lower than the original y-coordinate (5 - 2 = 3).
Therefore, the vertex of the function g(x) = f(-x) - 2 is (-6, 3).
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