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]
