Answer:
The parabola generated by the expression :

is the one that better represents a rain gauge above the ground.
Explanation:
The function:
a)

Direction of parabola: branches pointing up
Location of vertex relative to x-axis: below
So, the parabola doesn't depict a rain gauge off the ground
b)

Direction of parabola: branches pointing down
Location of vertex relative to x-axis: above
So, the parabola doesn't depict a rain gauge off the ground
c)
Direction of parabola: branches pointing up
Location of vertex relative to x-axis: two units above
So, the parabola depicts a rain gauge off the ground
d)

Direction of parabola: branches pointing up
Location of vertex relative to x-axis: right on the x-axis
So, the parabola doesn't depict a rain gauge off the ground (this is sitting on the ground)
e)

Direction of parabola: branches pointing up
Location of vertex relative to x-axis: below
So, the parabola doesn't depict a rain gauge off the ground