sloppycanada
  • sloppycanada
Write the equation of a parabola with a vertex at (-5, 2) and a directrix y = -1.
Mathematics
jamiebookeater
  • jamiebookeater
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sloppycanada
  • sloppycanada
\[x+5 = \frac{ 1 }{ 12 }(y-2)^2\]
amoodarya
  • amoodarya
directix is y=-1 so parabola is vertical (x+5)^2=4p(y-2)
sloppycanada
  • sloppycanada
Oh so I find 'p' now?

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anonymous
  • anonymous
Do you have any question choices? sorry haven't done these in a long time lol
sloppycanada
  • sloppycanada
http://gyazo.com/92c75a607eefcd67e67bf08e7368c6fa
anonymous
  • anonymous
I remember now! So we first put it in vertex form. Typical vertex form is ;\[y=a(x-h)^2+k\]
anonymous
  • anonymous
Keep in mind that h is x, and k is y, so \[(h,k) = (x,y)\]
anonymous
  • anonymous
this seems hard lol
anonymous
  • anonymous
So we have the vertex (and forgot to mention, that h,k is the vertex) (-5,2)
sloppycanada
  • sloppycanada
Yup! And since it's not at (0,0) it means I have to add things. If I remember correct, it's the opposite sign that you're supposed to use.
anonymous
  • anonymous
we put them in, and now we get what?
sloppycanada
  • sloppycanada
x+5 = (y-2)^2
sloppycanada
  • sloppycanada
But I still need the 4p
anonymous
  • anonymous
\[y=a(x+5)^2-2\]
anonymous
  • anonymous
Well we still have to find a, and note the answer choice that you picked is wrong :/
sloppycanada
  • sloppycanada
Which is something to do with "p"
anonymous
  • anonymous
hold on a sec...
sloppycanada
  • sloppycanada
Okay...?
anonymous
  • anonymous
SO a is the slope
anonymous
  • anonymous
Or the the rate of change
Loser66
  • Loser66
@amoodaray gave you the equation, why do you go on the complex way?
sloppycanada
  • sloppycanada
I'm not sure how to find 'p'
Loser66
  • Loser66
Is it not that "directrix y =-1" given?? and it gives you p = 1?? am I right?
Loser66
  • Loser66
|dw:1435884812050:dw|
sloppycanada
  • sloppycanada
Oh yeah..in that case... then my answer should be 1/4
Loser66
  • Loser66
and the equation of parabola is x^2 =4py in your case, just put the vertex in
Loser66
  • Loser66
yyyyyyyyyyyyes
sloppycanada
  • sloppycanada
x+5^2 = 1/4(y-2)^2?
Loser66
  • Loser66
Nope
Loser66
  • Loser66
\((x+5)^2=4(y-2)\) open parentheses
sloppycanada
  • sloppycanada
But that isn't one of my options...
Loser66
  • Loser66
\((x^2+10x+25) = 4y -8\)
Loser66
  • Loser66
\(4y=x^2+10x+33\) divide both sides by 4 what are your options?
sloppycanada
  • sloppycanada
http://gyazo.com/92c75a607eefcd67e67bf08e7368c6fa
Loser66
  • Loser66
hey, they don't open parentheses and our answer is b,
Loser66
  • Loser66
\((x+5)^2=4(y-2)\) divide both sides by 4, you get b
sloppycanada
  • sloppycanada
Okay.. Thanks!

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