Identify the vertex of the parabola: y=-x^{2}+5 x+6

Step 1 ：The given equation of the parabola is \(y = -x^{2} + 5x + 6\).

Step 2 ：The vertex of a parabola given by the equation \(y = ax^{2} + bx + c\) is given by the point \((-b/2a, f(-b/2a))\).

Step 3 ：In this case, \(a = -1\), \(b = 5\), and \(c = 6\).

Step 4 ：So, the x-coordinate of the vertex is \(-b/2a = -5/-2 = 2.5\).

Step 5 ：To find the y-coordinate of the vertex, we substitute \(x = 2.5\) into the equation of the parabola.

Step 6 ：Substituting \(x = 2.5\) into the equation gives \(y = -2.5^{2} + 5*2.5 + 6 = 12.25\).

Step 7 ：Final Answer: The vertex of the parabola is \(\boxed{(2.5, 12.25)}\).