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
