Aparabola has a vertex at (0,0). the equation for the directrix of the parabola is x = –4. in which direction does the parabola open? up down right left

 the direction that the parabola opens is right

We have that the directix is x=-4
this means the parabola opens left or right

if the vertex is to the left of the directix, then it opens to the left
if the vertex is to the right of the directix, then it opens to the right

see
(0,0) is vertex
x=-4 is directix
-4<0
vertex is to the right of directix
it opens to the right

What is the rest of the question?