Given that the maximum value of the function y = - x2 + ax-a / 4 + 1 / 2 (x belongs to [- 1,1]) is 2, find the value of A emergency

Given that the maximum value of the function y = - x2 + ax-a / 4 + 1 / 2 (x belongs to [- 1,1]) is 2, find the value of A emergency

The function y = - x2 + ax-a / 4 + 1 / 2 is - (x-a / 2) ^ 2 + A ^ 2 / 4-A / 4 + 1 / 2
When a / 2 belongs to [- 1,1], then when x = A / 2, the maximum value is a ^ 2 / 4-A / 4 + 1 / 2 = 2, A1 = 3 (rounding off), A2 = - 2
When a / 2 is on the left side of - 1, the maximum value is 2. When x = - 1, the function will enter the solution of the quadratic equation LZ with respect to a! I'm tired. The obtained a depends on whether it conforms to a / 2 ≤ - 1
When a / 2 is on the right side of 1 and band 1 is the maximum value, the calculated a depends on whether it conforms to a / 2 ≥ 1
This kind of problem has basic method, do a few times more can

The function y = x2-ax + A / 2 is known. When 0 ≤ x ≤ 1, the minimum value is m. find the maximum value of M

And it is also the case that when x = A / 2, the minimum value of M is m = A / 2-a-a-178 / 4 and 0 ≤ x ≤ 1, that is, 0 ≤ A / 2 ≤ 1, that is, 0 ≤ A / 2 ≤ 1, that is, 0 ≤ A / 2 ≤ 1, so 0 ≤ a ≤ A / 2 ≤ 2m = A / 2-2m = A / 2-A / 2-A / 2-A / 2-a-a-a-a-a-a-h-178 / 4 and 0 ≤ x ≤ 1, that is 0 ≤ A / 2 ≤ A / 2 ≤ 1 ≤ 1, so 0 ≤ a ≤ a ≤ 2 ≤ 2m = a / 2-A / 2-A / 2-A / 2-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-178, so, so, so, so, so, so, so 0 ≤ 0 ≤ 0 ≤ a ≤ 2m = 0+ 1-1)

Find the maximum value of function y = - x2 + ax on [- 1,3]

Solution:
It is easy to know that the axis of symmetry of the function is x = A / 2
① When a / 2

Given that the maximum value of the function y = - x2 + ax (0 ≤ x ≤ 1) is 2, find the value of the real number a

y=-x2+ax
=-(x-a/2)^2+a^2/4
(1),a/2