Question

Question #bab5e

Answer 1

Vertex is at `(2,-3)`, focus is at `(1.25, -3)` and
directrix is `x=2.75`

Explanation:

`y^2+6y+3x+3=0 or y^2+6y+9=-3x-3+9` or

`(y+3)^2= -3(x-2)or(y+3)^2= -4*3/4(x-2)`

`h=2 , k=-3,a= -3/4=-0.75` Vertex is at `(h,k)` or

at`(2,-3)` Since `a` is negative the parabola opens left.

Focus is at `(h-|a|),k) or (2-0.75, -3) or (1.25, -3)`

Directrix is `x=(h+|a|) or x= 2+0.75 or x=2.75`

graph{y^2+6y+3x+3=0 [-22.5, 22.5, -11.25, 11.25]}