逆算すりゃいいだろ
y=a(x-p)^2+q
=a(x^2-2px+p) + q
= ax^2 -2apx + (ap+q)

a=2
-2ap=-8 , p=2
ap+q=-5 , 2*2+q=-5 , 4+q=-5 , q=-9