F4 maths

consider a quadratic function y = -2(x-k)^2 + (k^2 - k + 2 ) where k is a positive constant .

a) if the max val of y = 4, find the val of k.
b) find value of y when x = 0
(a)
y gets the maximum value when -2(x-k)^2=0 ( k is a positive constant )
so x=k and maximum value is k^2 - k + 2
since max val of y = 4
k^2 - k + 2=4
k^2-k-2=0
(k-2)(k+1)=0
k=-1 (reject) or k=2
(b)
y=-2(x-2)^2 + (2^2 - 2 + 2 )
y=-2(x-2)^2 + 4
when x=0
y=-2(-2)^2+4
y=-4

a)The max value of y =4
so (k^2 - k + 2 )=4
k^2-k-2=0
(k-2)(k+1)=0
k=2 or k= -1(rejected)
b) When x=0
y = -2(0-2)^2 + (2^2 - 2 + 2 )
y= -4