The function g(x) = 3x2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)?(−6, −5)(−2, −5)(2, −5)(6, −5)

Answer:  The correct option is (C). (2, -5).Step-by-step explanation:  The given function is[tex]g(x)=3x^2-12x+7.[/tex]The vertex form of the function g(x) is [tex]g(x)=3(x-2)^2-5~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]We know that if the vertex form of a function f(x) is written as[tex]f(x)=a(x-h)^2+k,[/tex]then its vertex is (h, k).So, from equation (i), we can say that the vertex of function g(x) is (2, -5).Thus, (C) is the correct option.