Question

find the vertex,focus and equation of the direction of y=-1/16(x-6)^2+3

Y=1/2p(x-h)^2+k
p=8 h=6 k=3
so I now got

(6,3) when doing it over again. I now got
so vertex is (6,3), focus is (6,7) and directrix = y=-1
Is these corrections now right? Thank you for your help and checking my work!
Is this correct?

Answer 1

Recall that the parabola x^2 = 4py has
vertex (0,0)
focus (0,p)
directrix y = -p

Your equation can be written as

(x-6)^2 = -16(y-3)
so p = -4
Now just shift all the values by (6,3) and you get
vertex (6,3)
focus (6,-1)
directrix: y = 7

Answer 2

Thank you. That is what I had originally, and another help person said I was incorrect.