The equation $y^2+3=2(2x+y)$ represents a parabola with the vertex and focus at

The given equation can be rewritten as $(y-1{)}^2$ $=4\left(x-\frac{1}{2}\right)$ which is a parabola with its vertex $\left(\frac{1}{2},1\right)$ axis along the line y= 1, hence axis parallel to x-axis. Its

focus is $\left(\frac{1}{2}+1,1\right),\text{ i.e., }\left(\frac{3}{2},1\right)$.