Question

A parabola is defined by the equation x2 = 3/4 y. In which direction will the parabola open?

Answer 1

The equation of parabola is $x^2=\dfrac{3}{4}y$. 
The canonical equation of parabola is $y^2=2p x$ and this parabola has branches that go in positive direction of x-axis.

Since in your equation x is changed to y and y to x, then the branches of the parabola go in positive y-axis direction, the vertex is placed at the origin.