Question

find the vertex, focus, and directrix of the parabola and sketch its graph

y^2 = -6x

Answer 1

in standard form, this is a sidways parabola opening to the left...

4px = y^2
where p is the distance from the vertex to the parabola.

the vertex is at the origin (0, 0)
since 4p=-6, this implies p=-3/2
so your focus has coordinates (-3/2, 0)
the directrix is the same distance away but in the opposite direction of the focus. it has equation x=3/2

Answer 2

thanku

Answer 3

yw...:)