SOLUTION: The standard form equation of the parabola with vertex at (1, 2), latus rectum is 8, opens downward.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The standard form equation of the parabola with vertex at (1, 2), latus rectum is 8, opens downward.      Log On


   

Question 1170536: The standard form equation of the parabola with vertex at (1, 2), latus rectum is 8, opens downward.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Vertex form of the equation is

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

where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.

With the equation in this form, |4p| is also the length of the latus rectum.

With the parabola opening downward, p is negative, so 4p = -8.

Then you have all the parts you need to write the equation in vertex form:

y+=+%28%28-1%2F8%29%28x-1%29%5E2%29%2B2

Convert that to any desired form.