how do you calculate the focus and directrix from an equation hen its given in vertex form

Question

how do you calculate the focus and directrix from an equation hen its given in vertex form

Answer 1

The key is the P value.   If the parabola   is    f(x) = a ( x - v)² +h,    the P value is  P =  1/(4a).

 

The P value is both the distance from the vertex (v,h) to the focus and the distance from the vertex to the directrix.

 

So the focus is at   (v, h +  P) and the directrix is the line

 

y =    h - P.

 

The above is for an upward opening parabola.   Modifications are needed if the parabola opens down or to the left or to the right.  However, the P value remains the key.