Graph of a parabola #3

Question

Given the parabola having the equation x^2+4y+8x=4, find the vertex, focus, and the length of the latus rectum. Sketch the graph.

Answer 1

4y =-x^2 -8x +4

=-(x^2+8x +16) +20

y =(-1/4)(x+4)^2 +5 vertex is (-4,5)

focus (-4,4)

directrix y= 6

latus rectum 4

downward opening vertical parabola