quadric
locus of zeros of a quadratic polynomial (affine or projective, not necessarily real)
paraboloid
quadric surface of special kind
quadric surface
locus of zeros of a quadratic polynomial in a three-dimensional space (affine or projective, not necessarily real)
Klein quadric
quadric inside 5-dimensional projective space; the image of the Plücker embedding of the Grassmannian Gr₂(4)