Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created? A. f(x) = one fourth (x − 4)2 − 3
B. f(x) = one eighth (x + 4)2 − 3
C. f(x) = − one eighth (x − 4)2 + 3
D. f(x) = − one fourth (x + 4)2 − 3

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 )

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