Answer
Elliptic Paraboloid, axis: y
Work Step by Step
Rewriting,
$y=4x^{2}+2z^{2}$
$\displaystyle \frac{y}{1}=\frac{x^{2}}{(1/2)^{2}}+\frac{z^{2}}{(\sqrt{2})^{2}}$
Comparing the form with equations in Table 1, we find:
Elliptic Paraboloid
$\displaystyle \frac{z}{c}=\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$
In this case,
Traces in planes y=k are ellipses.
Traces in x=k and y=k are parabolas.
The variable raised to the first power (y) indicates the axis of the paraboloid.
