Determining whether a 3-dimensional equations creates a horizontal or non-horizontal plane?

Question

I am learning about graphing 3-dimensional shapes on x,y,z coordinates axis and am understanding everything for the most part. However, the thing that is continuously tripping me up is distinguishing the difference between horizontal and non horizontal planes and I am sure there is a general rule to follow, but I do not understand it visually.

Here are some examples I have seen that ask the type of question whether it is a horizontal or non-horizontal plane.

$$ Example (2): z = y^{2} - 2x^{2} $$

$$ Example (3): z = x^{2} $$

I am ruling that example 2 is a hyperbolic paraboloid.

This is the graph for example 2.

Answer 1

Only one plane equation number 4 with normal $(2,3,-1)$. The plane is $ax+by+cz=d$ with normal $(a,b,c)$ which helps you to answer your questions The graph of 3 is