Answer:
[tex]f(x)=(x-1)^2-6[/tex]
Step-by-step explanation:
The given quadratic function is
[tex]f(x)=x^2-2x-5[/tex]
We complete the square to obtain the vertex form;
Add and subtract half the coefficient of [tex]x[/tex]
[tex]f(x)=x^2-2x+(-1)^2-(-1)^2-5[/tex]
Factor by identifying the perfect square
[tex]f(x)=(x-1)^2-1-5[/tex]
Simplify to obtain the vertex form as
[tex]f(x)=(x-1)^2-6[/tex]
