Graph the parabolas and identify the axis, directrix, and focus: (y^2)+8x=0

Question

I know that the axis refers to the axis of symetry and the directrix is the same distance away from the vertex as the foucus is. I just don't know how to graph and identify all the parts from an equation like the one above.

Answer 1

Recall that the parabola

y^2 = 4px

has
vertex at (0,0)
focus at (p,0)
directrix at x = -p

(y^2)+8x=0
can be written as

y^2 = -8x
so p = -2
now just plug and chug.

It is clearly a parabola opening to the left with vertex at (0,0).

Answer 2

Thank you so much Steve!! just two questions, what does the variable "p" stand for/ represent and could I be able to represent the axis of symetry as an equation/point.

Answer 3

wait dose the axis even mean the axis of symetry??

Answer 4

yes, "axis" means the axis of symmetry.
and yes, your parabola has the x-axis as its axis of symmetry.

y = 0

Answer 5

thanks you so much!!

Answer 6

Can someone help me please.
How to find the equation of the axis of parabola and its length of the latus rectum having y-x²+8x=0?