PLEASE HELP The function f(x) = x2 − 2x + 8 is transformed such that g(x) = f(x − 2). Find the vertex of g(x). (1, 5) (3, 7) (1, 9) (−1, 7)

Answer: Second option.Step-by-step explanation: Given the function f(x): [tex]f(x) = x^2 - 2x + 8[/tex] Find [tex]f(x -2)[/tex]: [tex]f(x -2)=(x-2)^2 - 2(x-2) + 8[/tex] Remember that: [tex](a\±b)^2=a^2\±2ab+b^2[/tex] Then, simplifying: [tex]f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16[/tex] So the function g(x) is: [tex]g(x)=x^2-6x+16[/tex] Use the following formula to find the x-coordinate of the vertex of g(x): [tex]x=\frac{-b}{2a}[/tex] In this case:  [tex]a=1\\b=-6[/tex] Then: [tex]x=-\frac{-(-6)}{2(1)}=3[/tex] Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since [tex]g(x)=y[/tex], you get: [tex]y=3^2-6(3)+16=7[/tex] Therefore, the vertex of g(x) is: [tex](3,7)[/tex]