Question

Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

Answer 1

Focus: ( 4, 1 )
Directrix: y = 5
The vertex is always half of a distance between the focus and the directrix.
The vertex must be at: ( 4, 3 ),  h = 4,  k = 3
|p| is the distance between the vertex and the directrix ( which is over the vertex and p is negative ).  p = - 2
The equation:
( x - h )² = 4 p ( y - k )  
( x - 4 )² = -8 ( y - 3 )