AS3:Need Help with Vertical Scroller

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Hello ,
I am working on a Vertical scrolling Space shooter game, and i need help with 2 things which i really couldn’t find discussed anywhere:

1- need to make enemies which enters the stage from the top right corner that flies downwards through a parabolic shape
dives in, curves and rotates and goes back up through the top left corner.

stage size is 500×700 pixels


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y = ax^2 + b

Given points:


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Thanks Draco!