Question

The equation x=ay^2 describes a parabola if the value is a positive which way does the parabola open

Answer 1

You can always make up numbers and try to draw it. 
Let's say a = 1 for sake of simplicity.

If y=0 then x=0
If y=1 then x=1
If y=-1 then x=1
If y=2 then x=4
If y=-2 then x=4

As you can see, parabola opens to the right. Try drawing it to make sure you believe that. 
Keep in mind, parabola only opens to the right if you are using the conventional x-y plane, where x-axis is horizontal and y-axis is vertical.