How do you sketch the parabola #(x+2)^2=-20(y-5)# and find the vertex, focus, and directrix?

Question

3904 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-05T20:29:14

V(-2;5)
F(-2;0)
D: y=10 graph{(x+2)^(2)=-20 (y-5) [-12.375, 7.625, -4.68, 5.32]}

#(x-h)^2=4p(y-k)#
from here we know
vertex is V(h,k)
focus is F(h,k+p)
and the directrix is y=k-p

in
#(x+2)^(2)=-20 (y-5)#

#h=-2: k=5 and 4p=-20 -> p=-5#

then
V(h,k)=V(-2,5)

F(h,k+p) = F(-2,5-5) then F(-2,0)

and

directrix
#y=k-p -> y=5-(-5) -> y=10#