# Thread: Find the vertex, focus, and directrix of the parabola x + y^2 = 0

1. ## Find the vertex, focus, and directrix of the parabola x + y^2 = 0

The question asks me to find the vertex, focus, and directrix of the parabola:
x + y^2 = 0

I usually don't have problems with these types of questions, but this particular one is set up differently than the others that I have done.

I am not sure how to do it. Can anyone help?
Thanks.

2. Originally Posted by iluvmathbutitshard
The question asks me to find the vertex, focus, and directrix of the parabola:
x + y^2 = 0

I usually don't have problems with these types of questions, but this particular one is set up differently than the others that I have done.

I am not sure how to do it. Can anyone help?
Thanks.
Hi iluvmathbutitshard,

$\displaystyle x+y^2=0$

Put this in the form: $\displaystyle x=a(y-k)^2+h$

$\displaystyle x=-(y-0)^2+0$

Vertex is at $\displaystyle (0, 0)$. Since $\displaystyle a=-1$, the parabola opens left.

Focus is at $\displaystyle \left(h+\frac{1}{4a}, k\right)$

Directrix is $\displaystyle x=h-\frac{1}{4a}$

3. Thank you for answering. Is this correct?
Vertex: (0,0)
Focus: (-1/4, 0)
Directrix: x = 1/4

4. Originally Posted by iluvmathbutitshard
Thank you for answering. Is this correct?
Vertex: (0,0)
Focus: (-1/4, 0)
Directrix: x = 1/4
Looks good to me.

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### focus of x^2-y-2=0

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