The vertex form is
[tex]Y=\mleft(x-3\mright)^2-7[/tex]The form of the equation given is: Y=ax^2+bx+c
So, a=1, b=-6 and c=2
The vertex form is
[tex]Y=a\mleft(x-h\mright)^2+k[/tex]Where
[tex]h=\frac{-b}{2a}\text{ , and k=f(h)}[/tex]Then
[tex]h=\frac{-b}{2a}=\frac{-(-6)}{2\cdot1}=3[/tex][tex]k=f(h)=f(3)=(3)^2-6\cdot3+2[/tex]Then, using a,h and k:
[tex]Y=(x-3)^3-7[/tex]