Question

Which direction does the graph of the equation shown below open? Y^2-4x+4y-4=0

Answer 1

We have that
Y²-4x+4y-4=0
you can rewrite the equation as 
4x=y²+4y-4
x=(y²/4)+y-1
x=0.25*(y²+4y)-1
x=0.25*(y²+4y+4-4)-1
x=0.25*(y²+4y+4)-5
x=0.25*(y+2)²-5

the equation of the parabola is of the form
x=a(y-k)²+h
is a horizontal parabola
where
(h,k)-----> is the vertex-----> (-5,-2)
a=0.25
a> 0--------> open to the right

the answer is
the option D. Right

see the attached figure

Answer 2

The answer is D, right because you rewrite the equation to a x= equation. Just by doing that, you know the equation has to be left or right. When rewriting the equation, the slope is positive, therefore it is facing right