anonymous
  • anonymous
Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
y = -1/4 x^2 y^2 = -4x y^2 = -16x y = -1/16 x^2
Hero
  • Hero
Just a second...
anonymous
  • anonymous
no problem

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Hero
  • Hero
If given two points, the focus \((x_1, y_1)\) and the directrix \((x_2, y_2)\), you can insert them into the following formula: \((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\) then simplify afterwards to get the standard form of the parabola.
anonymous
  • anonymous
ok so what am i plugging in?
Hero
  • Hero
Oh, wrong question. You have the vertex and the focus, but not the directrix.
anonymous
  • anonymous
yea thats it
Hero
  • Hero
There's a process to find the directrix.
anonymous
  • anonymous
thats where im lost
Hero
  • Hero
Did you know that any point on the parabola is equidistant from the focus and the directrix?
Hero
  • Hero
This means that we can easily find the directrix since we have the vertex.
anonymous
  • anonymous
so how?
Hero
  • Hero
Well, basically, we know that the focus is (0,-4) and the vertex is (0,0). Since the focus is 4 units below the vertex, that means the directrix is four units above it.
Hero
  • Hero
We also know that the directrix is a horizontal line. In this case it will be y = 4. When we express the directrix as a point, it becomes \((x, 4)\)
anonymous
  • anonymous
oh ok i understand. so then from there i would plug it in to the equation you gave earlier?
Hero
  • Hero
So now we have the focus (0,-4) and the directrix (x,4). Plug those points into the formula above to find the standard form of the equation of the parabola. Yes.
anonymous
  • anonymous
do i need to solve for the missing x in the directrix
Hero
  • Hero
You don't. You insert the x into the formula in place of \(x_2\)
anonymous
  • anonymous
oh ok
Hero
  • Hero
At this point, it's probably a good idea to show the work you've done so far that way I can make sure you've done this step correctly.
anonymous
  • anonymous
how would i do that? im on the computer and im doing my work on paper...
Hero
  • Hero
Use the draw button or use \(LaTeX\)
anonymous
  • anonymous
ok ill have to draw it because my computer doesn't support latex
Hero
  • Hero
You can still type the LaTeX. It won't stop it from showing up on my end.
anonymous
  • anonymous
just give me a couple minutes
Hero
  • Hero
There's a draw button you can click BTW.
anonymous
  • anonymous
i know im just in the middle of doing the work
Hero
  • Hero
|dw:1439499465843:dw|
Hero
  • Hero
You should post what you've done now, that way you don't get too far ahead because one wrong mistake and then you'll have so much re-work to do.
anonymous
  • anonymous
ok ill start off with showing you what i plugged in: (x-0)^2 + (y-(-4))^2 = (x-x)^2 + (y-4)^2
Hero
  • Hero
Looks good so far.
anonymous
  • anonymous
x^2 + y^2 + 8y + 16 = y^2 - 8y +16
Hero
  • Hero
Yes you can do it that way, but there's a way to do it that avoids expanding.
Hero
  • Hero
What do you get for your final simplified result?
anonymous
  • anonymous
give me a sec
Hero
  • Hero
Once you get the correct result, I'll show you the other way to do it.
anonymous
  • anonymous
y=x^2/16
anonymous
  • anonymous
my answer would be D
Hero
  • Hero
D is correct, but you forgot the negative in your answer.
anonymous
  • anonymous
yea i forgot to type it
Hero
  • Hero
So \(LaTeX\) does not load for you?
anonymous
  • anonymous
no.... :(
Hero
  • Hero
If not, I can do it by hand and upload it that way.
anonymous
  • anonymous
sure
Hero
  • Hero
Hang on, I'm about to upload it
anonymous
  • anonymous
ok
Hero
  • Hero
|dw:1439501181613:dw|
anonymous
  • anonymous
ok i see. i understand it. thanks for all the help.
Hero
  • Hero
You're most welcome :) You're a great student.

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