Name:
Math 206A: Winter 2012
Quiz 1
Correct answers accompanied by incorrect or incomplete work will not receive full credit.
Good Luck!
1. For each of the following equations:
(i) Identify the name of the surface.
(ii) If appropriate, find the vertex or saddle point.
(iii) If the graph has an axis, indicate the direction of that axis.
(iv) Match it with a sketch (sketches are not necessarily oriented with respect to the usual placement
of x,y, and zaxes).
(It is not necessary to show work for this question. But if you get the question wrong, some work
might be worth partial credit.)
(a) 2x2
โ3y2
โz+ 2 = 0
(b) 4(x+ 2)2
โ4y2
โ(zโ1)2= 0
(c) 3x2+ 3z2= 27
(d) 3x2+y2+ 4z2= 1
(U) (V) (W)
(X) (Y) (Z)
