Given the equation of the parabola \(y = 2x^2 - 4x + 3\), find the vertex form of the parabola.

Step 1 ：Step 1: The general form of a parabola equation is \(y = ax^2 + bx + c\). In our given equation, \(a = 2\), \(b = -4\), and \(c = 3\).

Step 2 ：Step 2: The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola. To convert the given equation into vertex form, first factor out the coefficient \(a\) from the first two terms: \(y = 2(x^2 - 2x) + 3\).

Step 3 ：Step 3: To complete the square, add and subtract \((b/2a)^2\) inside the parentheses: \(y = 2[(x^2 - 2x + 1) - 1] + 3\).

Step 4 ：Step 4: Simplify the equation to get it into vertex form: \(y = 2[(x - 1)^2 - 1] + 3 = 2(x - 1)^2 + 1\).