Let's look at what's happening a little at a time:

FLIPS:

Let's look at Standard Parabola Guy:

y = x^2

Standard Parabola Guy  ...  opens towards positives

y = -x^2

upside-down Standard Parabola Guy  ...  opens towards negatives

 

Now, for Sideways Parabola Guy:

x = y^2

Sideways Parabola Guy  ...  opens towards positives

x = -y^2

upside-down Sideways Parabola Guy  ...  opens towards negatives

 

Try a couple (the stretching works the same):

Graphx = 3y^2
 
Graphx = -2y^2