Answer
Elliptical paraboloid (graph f).
Work Step by Step
Since, we have $z=-4x^2-y^2$
or, $4x^2+y^2=-z^2$
This can be re-written as:
$\dfrac{x^2}{(1/2)^2}+\dfrac{y^2}{1}=\dfrac{z}{-1}$
Since, the equation is a graph for an Elliptical paraboloid opening downward along the z-axis as shown in graph (f).
