## anonymous one year ago @freckles

1. anonymous

Using a directrix of y = -2 and a focus of (1, 6), what quadratic function is created? f(x) = 1/8(x - 1)2 - 2 f(x) = -1/8(x + 1)2 - 2 f(x) = -1/16(x + 1)2 - 2 f(x) = 1/16(x - 1)2 + 2

2. freckles

first little drawing: |dw:1433741364872:dw| I'm going to put the vertex midway between that horizontal line (Called y=-2) and the focus point (1,6) We will see if you are able to tell with the vertex point is...

3. freckles

|dw:1433741453855:dw|

4. freckles

the point I labeled V is the vertex it is midway between the directrix (y=-2 ) and the focus can you tell me the coordinates of the V point O have plotted for you

5. anonymous

(1, 2)

6. anonymous

am i right or am i misunderstanding

7. freckles

that's right

8. anonymous

okay now what?

9. freckles

|dw:1433741706545:dw| $4p(y-k)=(x-h)^2 \\ \text{ you said vertex was } (1,2)=(h,k) \\ 4p(y-2)=(x-1)^2$ now we need to find p is the distance between the vertex and the focus or also the distance between the vertex and the directrix p can be negative or positive depending on which way it is opened ours is opened up so it will be positive

10. freckles

|dw:1433741880300:dw| this distance is p

11. anonymous

so we do $\frac{ y_2 - y_1 }{ x_2 - x_1 }$ ?

12. freckles

no

13. freckles

it is a distance not a slope

14. anonymous

oh then is it 4?

15. freckles

yea

16. anonymous

ok

17. freckles

$4p(y-2)=(x-1)^2 \\ 4(4)(y-2)=(x-1)^2 \\ 16(y-2)=(x-1)^2 \\$ divide both sides by 16 and then add 2 on both sides

18. anonymous

$y - 2 = \frac{ (x - 1)^2}{ 16 }$ $y = \frac{ 2 + (x - 1)^2 }{ 16 }$ like this?

19. anonymous

oh so the answer is D

20. freckles

why does 2 have 16 underneath it ?

21. freckles

you add 2 on both sides after dividing 16 on both sides

22. anonymous

sorry that was a typo

23. freckles

$y=2+\frac{(x-1)^2}{16} \\ y=\frac{1}{16}(x-1)^2+2$

24. anonymous

Thanks can you help with a couple more?

25. anonymous

ill post them in a new thread so you can get more medals ?

26. freckles

I actually have to leave here I'm sorry

27. anonymous

okay np thnx for the help anyways

28. freckles

it's 1 am almost I have to wake up early

29. anonymous