Answer
Ellipse
Foci: $( -1/2,\pm \sqrt 3/2)$
Vertices: $(-1/2,\pm1)$
Work Step by Step
$4x^{2}+4x+y^{2}=0$
$\frac{(x+1/2)^{2}}{1/4}+y^2=1$, the equation of an ellipse.
$c^{2}=\sqrt {\frac{3}{4}}$
$c=\frac{\sqrt 3}{2}$
Foci: $( -1/2,\pm \sqrt 3/2)$
Vertices: $(-1/2,\pm1)$
