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

Question

sloppycanada · Answer

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

amoodarya · Answer

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

sloppycanada · Answer

Oh so I find 'p' now?

anonymous · Answer

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

sloppycanada · Answer

anonymous · Answer

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

anonymous · Answer

Keep in mind that h is x, and k is y, so
$$(h,k) = (x,y)$$

anonymous · Answer

this seems hard lol

anonymous · Answer

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

sloppycanada · Answer

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 · Answer

we put them in, and now we get what?

sloppycanada · Answer

x+5 = (y-2)^2

sloppycanada · Answer

But I still need the 4p

anonymous · Answer

$$y=a(x+5)^2-2$$

anonymous · Answer

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

sloppycanada · Answer

Which is something to do with "p"

anonymous · Answer

hold on a sec...

sloppycanada · Answer

Okay...?

anonymous · Answer

SO a is the slope

anonymous · Answer

Or the the rate of change

loser66 · Answer

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

sloppycanada · Answer

I'm not sure how to find 'p'

loser66 · Answer

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

loser66 · Answer

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