Answer
An Elliptical paraboloid opening downward along $z$-axis as represented by $\bf{Graph(f)}$
Work Step by Step
Given: $z=-4x^2-y^2$ ...(1)
or, $4x^2+y^2=-z^2$
Re-write as:
$\dfrac{x^2}{(1/2)^2}+\dfrac{y^2}{1}=\dfrac{z}{-1}$ ...(2)
Equation (2) shows a graph for an Elliptical paraboloid opening downward along $z$-axis as represented by $\bf{Graph(f)}$
