SOLUTION: Vertex at the origin, focus at (0, -4)

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Question 1191209: Vertex at the origin, focus at (0, -4)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You have asked about five of what are almost the same kind of question. Your text book should explain how this works, and you can do similarly if you'll use the definition of parabola, and the Distance Formula; unless you already know some favorite formula to just plug in the given values for your equation.

vertex (0,0)
Focus (0,-4)
Then directrix would be (x,4) or y=4.

Parabola has vertex as a maximum point and graph opens downward.

sqrt%28%28x-0%29%5E2%2B%28y-%28-4%29%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-4%29%5E2%29
-
x%5E2%2B%28y%2B4%29%5E2=%28y-4%29%5E2
x%5E2%2By%5E2%2B8y%2B16=y%5E2-8y%2B16
x%5E2%2B8y=-8y
highlight%28x%5E2=-16y%29

You could graph or sketch if you want.