To express \(2x^2 - 4x + 1\) in the form \(a(x + b)^2 + c\), we complete the square:

Start with the quadratic expression:

\(2x^2 - 4x + 1\)

Factor out the 2 from the first two terms:

\(2(x^2 - 2x) + 1\)

Complete the square inside the parentheses:

\(x^2 - 2x = (x - 1)^2 - 1\)

Substitute back:

\(2((x - 1)^2 - 1) + 1\)

Distribute the 2:

\(2(x - 1)^2 - 2 + 1\)

Simplify:

\(2(x - 1)^2 - 1\)

Thus, \(a = 2\), \(b = -1\), \(c = -1\).

The minimum point \(A\) is at \((1, -1)\).