Answer:
Option B [tex]f(x)=3(x-1)^{2}+6[/tex]
Step-by-step explanation:
we have
[tex]f(x)=3x^{2} -6x+9[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-9=3x^{2} -6x[/tex]
Factor the leading coefficient
[tex]f(x)-9=3(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)-9+3=3(x^{2} -2x+1)[/tex]
[tex]f(x)-6=3(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]f(x)-6=3(x-1)^{2}[/tex]
[tex]f(x)=3(x-1)^{2}+6[/tex] ------> equation in vertex form
the vertex is the point [tex](1,6)[/tex]
