Write the equation of a parabola with a vertex at (-5, 2) and a directrix y = -1.

- sloppycanada

Write the equation of a parabola with a vertex at (-5, 2) and a directrix y = -1.

- jamiebookeater

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- sloppycanada

\[x+5 = \frac{ 1 }{ 12 }(y-2)^2\]

- amoodarya

directix is y=-1 so parabola is vertical
(x+5)^2=4p(y-2)

- sloppycanada

Oh so I find 'p' now?

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## More answers

- anonymous

Do you have any question choices? sorry haven't done these in a long time lol

- sloppycanada

http://gyazo.com/92c75a607eefcd67e67bf08e7368c6fa

- anonymous

I remember now! So we first put it in vertex form.
Typical vertex form is ;\[y=a(x-h)^2+k\]

- anonymous

Keep in mind that h is x, and k is y, so
\[(h,k) = (x,y)\]

- anonymous

this seems hard lol

- anonymous

So we have the vertex (and forgot to mention, that h,k is the vertex) (-5,2)

- 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

we put them in, and now we get what?

- sloppycanada

x+5 = (y-2)^2

- sloppycanada

But I still need the 4p

- anonymous

\[y=a(x+5)^2-2\]

- anonymous

Well we still have to find a, and note the answer choice that you picked is wrong :/

- sloppycanada

Which is something to do with "p"

- anonymous

hold on a sec...

- sloppycanada

Okay...?

- anonymous

SO a is the slope

- anonymous

Or the the rate of change

- Loser66

@amoodaray gave you the equation, why do you go on the complex way?

- sloppycanada

I'm not sure how to find 'p'

- Loser66

Is it not that "directrix y =-1" given?? and it gives you p = 1?? am I right?

- Loser66

|dw:1435884812050:dw|

- sloppycanada

Oh yeah..in that case... then my answer should be 1/4

- Loser66

and the equation of parabola is x^2 =4py
in your case, just put the vertex in

- Loser66

yyyyyyyyyyyyes

- sloppycanada

x+5^2 = 1/4(y-2)^2?

- Loser66

Nope

- Loser66

\((x+5)^2=4(y-2)\)
open parentheses

- sloppycanada

But that isn't one of my options...

- Loser66

\((x^2+10x+25) = 4y -8\)

- Loser66

\(4y=x^2+10x+33\)
divide both sides by 4
what are your options?

- sloppycanada

http://gyazo.com/92c75a607eefcd67e67bf08e7368c6fa

- Loser66

hey, they don't open parentheses and our answer is b,

- Loser66

\((x+5)^2=4(y-2)\)
divide both sides by 4, you get b

- sloppycanada

Okay.. Thanks!

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