Question 360031
derivative of f should be 0 in 2 : f(x) = a(x-2)^2 + c
 
f(2) = c = 1
f(0) = 4a + c = -3 = 4a + 1 => a = -1
 
result : f(x) = -(x-2)^2 + 1 = -(x^2-4x+4) + 1 = -x^2 + 4x - 3
 
 
Verification : f(0) = -3, f'(x) = -2x+4 => f'(2) = 0 (maximum)