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

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 ) 

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.