HELP PLEASEbut only answer if you're going to show work, and how you got the answer please!!! will give brainiest if you show work

We have the following equation:
 y = -2x2 + 2x + 2
 We look for the vertex of the parabola. For this, we derive the given equation:
 y '= - 4x + 2
 We match zero:
 0 = -4x + 2
 We clear x:
 4x = 2
 x = 2/4
 x = 1/2
 We evaluate the function for x = 1/2:
 y = -2 * (1/2) ^ 2 + 2 * (1/2) + 2
 y = 2.5
 The vertice of the parabola is:
 (x, y) = (1/2, 2.5)
 We now look for the value of the function for x = 6:
 y = -2 * (6) ^ 2 + 2 * (6) + 2
 y = -58
 Answer:
 The vertice of the parabola is:
 (x, y) = (1/2, 2.5)
 the value of the function for x = 6 is:
 y = -58