SOLUTION: Determine the equation of a parabola where the vertex is (4,3) and focus is at (4,-1).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Determine the equation of a parabola where the vertex is (4,3) and focus is at (4,-1).       Log On


   

Question 1147614: Determine the equation of a parabola where the vertex is (4,3) and focus is at (4,-1).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The vertex and focus have the same x coordinate, so the parabola opens up or down; since the focus is below the vertex, it opens down.

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

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

where p is the directed distance from the vertex to the focus.

The directed distance from the vertex to the focus in this example is -4, so 4p = -16. With the vertex at (4,3), the equation is then

y-3+=+%28-1%2F16%29%28x-4%29%5E2

or

y+=+%28-1%2F16%29%28x-4%29%5E2%2B3