Let's compare with graphs.
Find the vertex of each.
s(x)=2x^2+0x-4
x=-b/2a
x=0/4=0
0-4=-4
(0,-4)=Vertex.
f(x)=x^2+0x-0
x=0/2=0
0+0-0=0
(0,0)=Vertex.
f(6)=36
s(6)=68