Find the focus of the following Parabola:

y=-1/4x^2

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  (0, -1)

Step-by-step explanation:

Compare the equations ...

  y = -1/4x^2

  y = 1/(4p)(x -h)^2 +k

You can see that (h, k) = (0, 0), and that p = -1.

The value of p is the distance from the vertex to the focus. Here, the parabola opens downward, and the focus is 1 unit below the vertex.

The focus is (0, -1).

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Additional comment

Every point on the parabola is the same distance from the focus as it is from the directrix. A couple of points that are easy to check are the vertex, and the points on the same horizontal line as the focus. This check can tell you if we have properly found the focus.