Find the vertex of the function \(f(x) = -2x^2 + 4x + 5\).

Step 1 ：The vertex form of a quadratic function is \(f(x) = a(x - h)^2 + k\), where the vertex of the parabola is at point (h, k).

Step 2 ：The x-coordinate of the vertex can be found using the formula \(h = -\frac{b}{2a}\). For the given function, a = -2 and b = 4, so \(h = -\frac{4}{2*(-2)} = 1\).

Step 3 ：Substitute x = 1 into the function to find y-coordinate of the vertex: \(f(1) = -2*1^2 + 4*1 + 5 = 7\).

Step 4 ：Therefore, the vertex of the function is at point (1, 7).