The vertex of the function defined as [tex]g(x) = f(-x) -2[/tex] is 3.
Since quadratic functions are even functions, vertices have the following property in the case of a reflection on the y-axis:
[tex]f(x) = f(-x)[/tex] (1)
If we know that [tex]x = 4[/tex], [tex]f(x) = 5[/tex] and [tex]g(x) = f(-x) -2[/tex], then the vertex of the function is:
[tex]f(-x) = 5[/tex]
[tex]g(x) = 5 - 2[/tex]
[tex]g(x) = 3[/tex]
The vertex of the function defined as [tex]g(x) = f(-x) -2[/tex] is 3. [tex]\blacksquare[/tex]
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