# What is the focus,directrix, axis and vertex of the equation x-2=1/8 (y+1)^2. Graph too if possible

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Expert Answers

baxthum8 | Certified Educator

`x - 2 = (1/8)(y+1)^2`

Parabola opening towards right as x is positive and y is squared.

**Vertex = (2, -1)** from general (graphing) form of a parabola

Which means **axis is horizontal: y = -1**

Multiply both sides by 8 to isolate `(y+1)^2`

you get `8(x - 2) = (y + 1)^2`

this means 4p = 8, (from `(x-h)^2 = 4p(y - k))`

therefore p = 2 which means focus is 2 units to right of vertex,

focus: (4, -1)and directrix is vertical line passing through point 2 units to left of vertex

directrix: x = 0

*(sorry, can't seem to get graph for x= on this system, hopefully you can follow from information to determine a graph now that you know which way it opens and vertex)*