Write an Equation for the Parabola with Vertex at the Origin

Multiple Choice

Write an equation for the parabola with vertex at the origin.
-Through $( \sqrt { 2 } , 2 )$ , opening upward

A) $x = y ^ { 2 }$
B) $x = \frac { \sqrt { 2 } } { 2 } y ^ { 2 }$
C) $y = x ^ { 2 }$
D) $y = 2 x ^ { 2 }$