Find the maximum value of the quadratic function \(f(x) = -2x^2 + 4x + 3\).

Step 1 ：The quadratic function \(f(x) = ax^2 + bx + c\) reaches its maximum or minimum value at \(x = -\frac{b}{2a}\). So, let's calculate \(x = -\frac{b}{2a}\) for \(f(x) = -2x^2 + 4x + 3\).

Step 2 ：\(-\frac{b}{2a} = -\frac{4}{2*(-2)} = 0.5\)

Step 3 ：Substitute \(x = 0.5\) into the function \(f(x) = -2x^2 + 4x + 3\) to find the maximum value.

Step 4 ：\(f(0.5) = -2(0.5)^2 + 4*0.5 + 3 = 3.5\)