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

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

2. amoodarya

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

Oh so I find 'p' now?

4. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

this seems hard lol

9. anonymous

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

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.

11. anonymous

we put them in, and now we get what?

x+5 = (y-2)^2

But I still need the 4p

14. anonymous

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

15. anonymous

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

Which is something to do with "p"

17. anonymous

hold on a sec...

Okay...?

19. anonymous

SO a is the slope

20. anonymous

Or the the rate of change

21. Loser66

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

I'm not sure how to find 'p'

23. Loser66

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

24. Loser66

|dw:1435884812050:dw|

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

26. Loser66

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

27. Loser66

yyyyyyyyyyyyes

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

29. Loser66

Nope

30. Loser66

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

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

32. Loser66

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

33. Loser66

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

35. Loser66

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

36. Loser66

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