1. ## parabolas

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

x + y^2 = 0

2. Originally Posted by kenzie103109
find the vertex, focus, and directrix of the parabola and sketch its graph

x + y^2 = 0
The equation of your parabola would be :

$\displaystyle (y-k)^2=4p(x-h)$

where (h,k) is the vertex

Put your given equation in the above form. This should be explained in your book. Show your work if you have any problems.

3. Originally Posted by kenzie103109
find the vertex, focus, and directrix of the parabola and sketch its graph

x + y^2 = 0
as mentioned since $\displaystyle h=0$ and $\displaystyle k=0$

then you have a vertex at $\displaystyle V(0.0)$

so now we have the equation of $\displaystyle y^2 = 4ax$ here $\displaystyle 4a= -1$ so $\displaystyle a = -\frac{1}{4}$

Focus at $\displaystyle (a,0)$ so $\displaystyle F(-\frac{1}{4},0)$

Directix at $\displaystyle x = -a$ so $\displaystyle x =\frac{1}{4}$ is the Directix

note some books use $\displaystyle a$ versus $\displaystyle p$ as the variable