Question

Find the vertex, focus, and directrix of the parabola. then sketch the parabola. (x + 2) + (y − 3)2 = 0

Answer 1

yay
alrighty so this is a parabola that opens to the left or right

for
(y-k)²=4p(x-h)
the vertex is (h,k)
p is the distance from the vertex to the focus
also  it is the disatnce from the vertex to the directix

when p is positive, the focus is to the right of the vertex and dirextix
when p is negative, the focus is to the left of vertex and directix

vertex is between focus and directix


alrighty, get into the form

minus (x+2) both sides
(y-3)²=-1(x+2)
$(y-3)^2=4(\frac{-1}{4})(x-(-2))$
vertex is (-2,3)
p is negative and is equal to -1/4
focus is to left of directix and vertex

alrighty
so since focus is to the left of vertex, and it is 1/4 units to the left, the focus is (-2.25,3)

directx is to the right of vertex, it is 1/4 units to the right so the directix is x=-1.75


vertex is (-2,3)
focus is (-2.25,3)
directix is x=-1.75