I need help finding the focus of the parabola (equation in post)

Question

tabithax3 · Answer

$$-4(x+\frac{ 1 }{ 2 })^{2}=y$$

anonymous · Answer

To find the focus in this situation, arrange the equation in the following form:

x^2 = whatever is on the right side.

After you have done that, we'll take a look at what you have and help you find the focus.

anonymous · Answer

Typically, when the equation is in the form x^2 = 4ay, the focus would be (0, a).  However, there may be other parameters in your equation that we need to look at.

tabithax3 · Answer

@EulersEquation i don't understand. do i have to leave x by itself?

anonymous · Answer

I don't know how deep you are into finding the vertices of a parabola, but typically, you want your equation to look like this:

x^2 = 4ay,

as I said before.  Can you get it into that form?

mertsj · Answer

$$(x+\frac{1}{2})^2=\frac{-1}{4}y$$

mertsj · Answer

This is of the form :
$$x^2=4py$$

mertsj · Answer

The focal point is p units above or below the vertex depending on whether it opens up or down.

tabithax3 · Answer

@Mertsj thank you!

mertsj · Answer

yw

tabithax3 · Answer

@EulersEquation thank you for the help! i was stressing out on what you were telling me, and you were giving me simple instructions, forgive me on that. but my answer is $$(-\frac{ 1 }{ 2 }, -\frac{ 1 }{ 16 })$$

anonymous · Answer

Tabithax is correct: the x-coordinate is h, when in the form (x - h)^2.  So the x-coordinate is -(1/2).

mertsj · Answer

Oh yes.  I forgot about the 1/2.  Sorry.

tabithax3 · Answer

@EulersEquation thank you for clarifying! @Mertsj it's fine :)
you two helped me a lot. i wish this site would allow me to give both of you a "best response"