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anonymous
 one year ago
Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 4).
anonymous
 one year ago
Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 4).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = 1/4 x^2 y^2 = 4x y^2 = 16x y = 1/16 x^2

Hero
 one year ago
Best ResponseYou've already chosen the best response.1If 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
 one year ago
Best ResponseYou've already chosen the best response.0ok so what am i plugging in?

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Oh, wrong question. You have the vertex and the focus, but not the directrix.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1There's a process to find the directrix.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Did you know that any point on the parabola is equidistant from the focus and the directrix?

Hero
 one year ago
Best ResponseYou've already chosen the best response.1This means that we can easily find the directrix since we have the vertex.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Well, 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
 one year ago
Best ResponseYou've already chosen the best response.1We 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
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i understand. so then from there i would plug it in to the equation you gave earlier?

Hero
 one year ago
Best ResponseYou've already chosen the best response.1So 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
 one year ago
Best ResponseYou've already chosen the best response.0do i need to solve for the missing x in the directrix

Hero
 one year ago
Best ResponseYou've already chosen the best response.1You don't. You insert the x into the formula in place of \(x_2\)

Hero
 one year ago
Best ResponseYou've already chosen the best response.1At 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
 one year ago
Best ResponseYou've already chosen the best response.0how would i do that? im on the computer and im doing my work on paper...

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Use the draw button or use \(LaTeX\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok ill have to draw it because my computer doesn't support latex

Hero
 one year ago
Best ResponseYou've already chosen the best response.1You can still type the LaTeX. It won't stop it from showing up on my end.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just give me a couple minutes

Hero
 one year ago
Best ResponseYou've already chosen the best response.1There's a draw button you can click BTW.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know im just in the middle of doing the work

Hero
 one year ago
Best ResponseYou've already chosen the best response.1You 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 rework to do.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok ill start off with showing you what i plugged in: (x0)^2 + (y(4))^2 = (xx)^2 + (y4)^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x^2 + y^2 + 8y + 16 = y^2  8y +16

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Yes you can do it that way, but there's a way to do it that avoids expanding.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1What do you get for your final simplified result?

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Once you get the correct result, I'll show you the other way to do it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my answer would be D

Hero
 one year ago
Best ResponseYou've already chosen the best response.1D is correct, but you forgot the negative in your answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea i forgot to type it

Hero
 one year ago
Best ResponseYou've already chosen the best response.1So \(LaTeX\) does not load for you?

Hero
 one year ago
Best ResponseYou've already chosen the best response.1If not, I can do it by hand and upload it that way.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1Hang on, I'm about to upload it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i see. i understand it. thanks for all the help.

Hero
 one year ago
Best ResponseYou've already chosen the best response.1You're most welcome :) You're a great student.
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