SOLUTION: Write and equation for the parabola with a vertex (0,0) and focus (0,-1/12)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write and equation for the parabola with a vertex (0,0) and focus (0,-1/12)       Log On


   

Question 747686: Write and equation for the parabola with a vertex (0,0) and focus (0,-1/12)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The focus is below the vertex, so this vertex is a maximum. You expect the coefficient on x^2 to be negative.

A general equation for a parabola having vertex on the origin is 4py=x%5E2, where p is the focal length, distance between the focus and the vertex. In your exercise, p=1%2F12. See your textbook and http://en.wikipedia.org/wiki/Parabola .

The equation for the described parabola is highlight%28y=%281%2F%284%2Ap%29%29%2Ax%5E2%29, and as said, since the vertex is a maximum, we must have %281%2F%284p%29%29%3C0, so we have:
y=-%281%2F%284%2A%281%2F12%29%29%29x%5E2
y=-%2812%2F4%29x%5E2
highlight%28y=-3x%5E2%29.