Answer:
The vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=4+x^2-2x[/tex]
The vertex form is
[tex]f(x)=(x-h)^2+k[/tex]
Rewrite the given function
[tex]f(x)=(x^2-2x)+4[/tex]
[tex]-\frac{b}{2a}=-\frac{-2}{2(1)}=1[/tex]
Add and Subtract [tex](-\frac{b}{2a})^2[/tex].
[tex]f(x)=(x^2-2x+1)+4-1[/tex]
Use [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]f(x)=(x-1)^2+3[/tex]
Therefore the vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].
