(1 point) On a piece of paper, sketch each of the following surfaces: (i) z = x2 +y2 +6 (ii) z = 3x2 Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (z = x2 2 + 6): Cross sections with x fixed give a downward opening parabola in a plane parallel to the yz-plane a downward opening parabola in a plane parallel to the xz-plane a downward opening parabola in a plane parallel to the xy-plane Cross sections with y fixed give Cross sections with z fixed give (b) For (ii) (z = 3x2): Cross sections with x fixed give Cross sections with y fixed give Cross sections with z fixed give an empty set, or one or two vertical lines in a plane parallel to the yz-plane> an empty set, or one or two vertical lines in a plane parallel to the xz-plane a downward opening parabola in a plane parallel to the xy-plane
