The vertex form of a parabola is given by \( y = a(x - h)^2 + k \). Convert the quadratic function \( y = 2x^2 - 4x + 3 \) into its vertex form and identify the vertex. Then, determine the value of \( y \) when \( x = \frac{7}{2} \). Let's think step by step and output the final answer within \boxed{}.
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