easy
ok, so
for y=a(x-h)^2+k
the vertex is (h,k)
given that the the vertex is (-2,-20)
y=a(x-(-2))^2+(-20)
y=a(x+2)^2-20
find a
when x=0, then y=-12
-12=a(0+2)^2-20
-12=a(2)^2-20
8=4a
2=a
equation is
y=2(x+2)^2-20
if the last term is positive, then maybe y=2(x+2)^2+(-20)?
unless you typed something wrong, then you are right that the last term is -20