Answer : A) \(f(x) = (x-1)^2 - 7\)
Standard form of equation is \(f(x) = x^2 - 2x - 6\)
The vertex form of equation is \(y= (x-h)^2 + k\)
where (h,k) is the vertex
To find x coordinate of vertex we use formula \(h =\frac{-b}{2a}\)
\(f(x) = x^2 - 2x - 6\), a=1, b=-2 and c=-6
Plug in the values
\(h =\frac{-b}{2a}=\frac{-(-2)}{2*1}= 1\)
Now plug in x=1 in the equation
\(k =f(x) = 1^2 - 2(1) - 6 = 1-2-6= -7\)
h= 1 and k=-7
The vertex form of equation is \(y= (x-h)^2 + k\)
Plug in the values h=1 and k=-7
\(f(x)= (x-1)^2 - 7\)
