y=2x²+8x+k is probably what was intended here, because y=2x²+8x+y doesn’t make sense in this context. k is a constant which we don’t know but we can use it to show the vertex. y=2(x²+4x+4-4)+k=2[(x+2)²-4]+k.
So y=2(x+2)²-8+k, y+8-k=2(x+2)². In this form we see the vertex is at (-2,k-8).
Other significant coordinates would be the x and y intercepts. The y intercept is (0,k). The x intercepts (if any) are the zeroes of the quadratic.
If there are no x intercepts, then putting x=1 gives us another point (1,k+10).