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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).

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  1. anonymous
    • one year ago
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    y = -1/4 x^2 y^2 = -4x y^2 = -16x y = -1/16 x^2

  2. Hero
    • one year ago
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    Just a second...

  3. anonymous
    • one year ago
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    no problem

  4. Hero
    • one year ago
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    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.

  5. anonymous
    • one year ago
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    ok so what am i plugging in?

  6. Hero
    • one year ago
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    Oh, wrong question. You have the vertex and the focus, but not the directrix.

  7. anonymous
    • one year ago
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    yea thats it

  8. Hero
    • one year ago
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    There's a process to find the directrix.

  9. anonymous
    • one year ago
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    thats where im lost

  10. Hero
    • one year ago
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    Did you know that any point on the parabola is equidistant from the focus and the directrix?

  11. Hero
    • one year ago
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    This means that we can easily find the directrix since we have the vertex.

  12. anonymous
    • one year ago
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    so how?

  13. Hero
    • one year ago
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    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.

  14. Hero
    • one year ago
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    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 \((x, 4)\)

  15. anonymous
    • one year ago
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    oh ok i understand. so then from there i would plug it in to the equation you gave earlier?

  16. Hero
    • one year ago
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    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.

  17. anonymous
    • one year ago
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    do i need to solve for the missing x in the directrix

  18. Hero
    • one year ago
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    You don't. You insert the x into the formula in place of \(x_2\)

  19. anonymous
    • one year ago
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    oh ok

  20. Hero
    • one year ago
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    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.

  21. anonymous
    • one year ago
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    how would i do that? im on the computer and im doing my work on paper...

  22. Hero
    • one year ago
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    Use the draw button or use \(LaTeX\)

  23. anonymous
    • one year ago
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    ok ill have to draw it because my computer doesn't support latex

  24. Hero
    • one year ago
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    You can still type the LaTeX. It won't stop it from showing up on my end.

  25. anonymous
    • one year ago
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    just give me a couple minutes

  26. Hero
    • one year ago
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    There's a draw button you can click BTW.

  27. anonymous
    • one year ago
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    i know im just in the middle of doing the work

  28. Hero
    • one year ago
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    |dw:1439499465843:dw|

  29. Hero
    • one year ago
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    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.

  30. anonymous
    • one year ago
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    ok ill start off with showing you what i plugged in: (x-0)^2 + (y-(-4))^2 = (x-x)^2 + (y-4)^2

  31. Hero
    • one year ago
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    Looks good so far.

  32. anonymous
    • one year ago
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    x^2 + y^2 + 8y + 16 = y^2 - 8y +16

  33. Hero
    • one year ago
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    Yes you can do it that way, but there's a way to do it that avoids expanding.

  34. Hero
    • one year ago
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    What do you get for your final simplified result?

  35. anonymous
    • one year ago
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    give me a sec

  36. Hero
    • one year ago
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    Once you get the correct result, I'll show you the other way to do it.

  37. anonymous
    • one year ago
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    y=x^2/16

  38. anonymous
    • one year ago
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    my answer would be D

  39. Hero
    • one year ago
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    D is correct, but you forgot the negative in your answer.

  40. anonymous
    • one year ago
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    yea i forgot to type it

  41. Hero
    • one year ago
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    So \(LaTeX\) does not load for you?

  42. anonymous
    • one year ago
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    no.... :(

  43. Hero
    • one year ago
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    If not, I can do it by hand and upload it that way.

  44. anonymous
    • one year ago
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    sure

  45. Hero
    • one year ago
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    Hang on, I'm about to upload it

  46. anonymous
    • one year ago
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    ok

  47. Hero
    • one year ago
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    |dw:1439501181613:dw|

  48. anonymous
    • one year ago
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    ok i see. i understand it. thanks for all the help.

  49. Hero
    • one year ago
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    You're most welcome :) You're a great student.

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