Find the vertex of the function \(f(x) = 2x^2 - 4x + 1\).

Step 1 ：Step 1: The vertex form of a parabola is \(f(x) = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola. Let's convert the given function into the vertex form.

Step 2 ：Step 2: The function \(f(x) = 2x^2 - 4x + 1\) can be rewritten as \(f(x) = 2(x^2 - 2x) + 1\).

Step 3 ：Step 3: Adding and subtracting \(1\) inside the parenthesis, we get \(f(x) = 2[(x^2 - 2x + 1) - 1] + 1\).

Step 4 ：Step 4: Now, \(f(x) = 2[(x - 1)^2 - 1] + 1\).

Step 5 ：Step 5: Simplifying further, \(f(x) = 2(x - 1)^2 - 2 + 1\), which is \(f(x) = 2(x - 1)^2 - 1\).

Step 6 ：Step 6: So, the vertex \((h, k)\) of the function is \((1, -1)\).