New Year's Count Down.

If f(x)=x²-10x-28
Then f(x)=(x-5)²-3
Therefore the axis of symmetry is x=5(a≤x≤a+4).
a) a+4<5
Therefore a<1
At x=a
Minimum value : (a-5)²+3
b) a≤5≤a+4
Therefore -4≤a≤5
Thus x=5
Minimum value : 3
c) a>5
At x=a+4
Minimum value : (a-1)²+3
If x=2
Minimum value : 6

I'm pretty sure I did it correctly...