## Barrelracing one year ago What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6? a) -1/6x^2 +4/3x + 11/6 b) 1/6x^2 - 4/3x - 11/6 c) 3/50x^2 + 11/25x + 3/5 d) 2/50x^2 + 11/25 + 2/5

1. freckles

|dw:1444325601632:dw| the vertex is halfway between the directrix and the focus

2. freckles

what number is midway between -3 and -6?

3. Barrelracing

-4 and -5

4. freckles

but what number is midway between -3 and -6? hence do you know how to find the average of -3 and -6?

5. Barrelracing

oh no i dont

6. freckles

the average of two numbers is the sum of the numbers divided by 2

7. Barrelracing

i got -1.5

8. freckles

-3+(-6)=-9 -9/2 equals -4.5 not -1.5

9. Barrelracing

oh i did wrong sorry

10. freckles

-4.5 makes since because this number is halfway between -4 and -5

11. freckles

sense*

12. freckles

it is also the number halfway between -3 and -6

13. freckles

|dw:1444325972949:dw|

14. freckles

so our parabola looks like this roughly : |dw:1444326013448:dw|

15. freckles

anyways the equation is $4p(y-k)=(x-h)^2 \\ \text{ where } (h,k) \text{ is the vertex } \\ \text{ and } p \text{ is the distance between the vertex and the focus } \\ \text{ we also have } p>0 \text{ here since the vertex is above the directrix } \\ \text{ if it was the other way around we would have } p<0$

16. Barrelracing

ok thank you i get it now