SOLUTION: write the equation of a parabola with a vertex at the origin and a focus of (0, -3).

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Question 1160185: write the equation of a parabola with a vertex at the origin and a focus of (0, -3).
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The vertex form of the equation of a parabola that opens up or down with vertex (h,k) is

y-k+=+%281%2F%284p%29%29%28x-h%29%5E2

where p is the directed distance (that is, it might be negative) from the vertex to the focus.

In this problem, all the information required to write the equation is given to you; there is no work to be done other than plug in the numbers.

The vertex is (0,0); the directed distance from the vertex (0,0) to the focus (0,-3) is -3, so p = -3.

Plug in the numbers:

y-%28-3%29+=+%281%2F%284%28-3%29%29%29%28x-0%29%5E2

y%2B3+=+%28-1%2F12%29x%5E2

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Oops! Tutor @MathTherapy spotted my error.... The vertex is (0,0), not (0,-3). So

y-0+=+%281%2F%284%28-3%29%29%29%28x-0%29%5E2

y+=+%28-1%2F12%29x%5E2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

write the equation of a parabola with a vertex at the origin and a focus of (0, -3).