## itsmichelle29 one year ago I give medals to helpers thanks Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.

1. itsmichelle29

can you guys help me plz

2. anonymous

y = -1/16(x - (-2))^2 +9.

3. itsmichelle29

I dont understand

4. itsmichelle29

Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand. Can you give me this answer

5. misty1212

HI!!

6. itsmichelle29

7. misty1212

no one likes these conic section questions, but they are not that hard really

8. misty1212

first off, do you know what the parabola would look like (open right, left, up or down?)

9. itsmichelle29

Nope

10. misty1212

hmm that is a problem lets plot the focus and graph the directrix

11. itsmichelle29

okay

12. misty1212

|dw:1434503255264:dw|

13. misty1212

you can see that the focus \((-2,5)\) is BELOW the directrix, which is a horizontal line that means the parabola will open DOWN

14. itsmichelle29

Ohhh okay

15. misty1212

the next thing we need to do is find the vertex do you know how to find it ?

16. itsmichelle29

No ='(

17. misty1212

it is the point half way between \((-2,5)\) and \(y=13\) what is half way between \(5\) and \(13\)?

18. itsmichelle29

9

19. misty1212

right (got logged out somehow)

20. misty1212

that means the vertex is \((-2,9)\)

21. misty1212

now we are almost done

22. itsmichelle29

OKAY

23. itsmichelle29

so now what ?

24. misty1212

since the vertex is \((-2,5)\) and it opens down, it will look like \[4p(y-9)=(x+2)^2\] all we need is \(p\) and to note that \(4p\) will be negative since it opens down

25. misty1212

oops i meant "since the vertex is \((-2,9)\) my mistake

26. itsmichelle29

no its -2 5

27. misty1212

to find \(p\) is also easy it is the distance between the focus \((-2,5)\) and the vertex \((-2,9)\)

28. itsmichelle29

ohhh n.m.

29. misty1212

how far from \(5\) to \(9\)?

30. misty1212

did i lose you?