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
