Identify the graph of the function $f ( x , y ) = 3 - x ^ { 2 } - y ^ { 2 }$ .
A)Cone
B)Paraboloid
C)Ellipsoid
D)Hyperboloid of one sheet
E)Hyperboloid of two sheets
F)Hyperbolic cylinder
G)Elliptic cylinder
H)Parabolic cylinder

Question

Quizplus · Accepted Answer

The function $f(x, y) = 3 - x^2 - y^2$ represents a paraboloid because it is a quadratic function in both $x$ and $y$, and all the quadratic terms have the same sign, indicating that it opens downwards from a maximum point.

Identify the Graph of the Function f(x,y)=3−x2−y2f ( x , y ) = 3 - x ^ { 2 } - y ^ { 2 }f(x,y)=3−x2−y2

Identify the Graph of the Function $f ( x , y ) = 3 - x ^ { 2 } - y ^ { 2 }$