## anonymous one year ago What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1? f(x) = −one fourth (x − 5)2 + 1 f(x) = one fourth (x − 5)2 + 1 f(x) = −one fourth (x − 5)2 f(x) = one fourth (x − 5)2

1. freckles

i like to draw first... |dw:1438724043667:dw| the vertex will be halfway between the directrix and the focus

2. freckles

|dw:1438724120865:dw| what are the coordinates for V

3. anonymous

(0,5)?

4. freckles

|dw:1438724184117:dw| but isn't (0,5) on the y-axis

5. anonymous

idk that's why im asking you i have no idea how to do any of this CX

6. freckles

so you haven't ever plotted points in your class?

7. anonymous

i have but i never actually paid attention. im one of those kids that sleep in class tbh . and now im making up for it :/

8. freckles

(x,y) means we are going to travel horizontal x units (note: the sign of x tells us which way we will travel horizontally) means we are going to travel vertically y units (note: the sign of y tells which way we will travel vertically)

9. freckles

(0,5) tells us we will go 0 units left or right horizontally tells us we will go 5 units up

10. anonymous

oh so we would be going (5,0) ? Because you're going 5 units to the right and 0 up ?

11. freckles

right

12. freckles

the vertex is (5,0)

13. anonymous

what do i do with that?

14. anonymous

p.s im also really bad at graphing even if i was good at algebra CX

15. freckles

|dw:1438724452936:dw|

16. anonymous

so (5,-1)?

17. freckles

(5,-1) is the focus you were given this y=1 is the directrix (5,0) is what you found to be the vertex and we just determined p was negative since the parabola is opened down you can find the other part of p by finding the vertical distance between the vertex and the dirextrix which is 1 so p=-1 since we determined it was going to be negative already $(x-h)^2=4p(y-k) \\ \text{ divide } 4p \text{ on both sides } \frac{1}{4p}(x-h)^2=y-k \\ \text{ add } k \text{ on both sides } \\ y=\frac{1}{4p}(x-h)^2+k$

18. freckles

you have already determined the vertex (h,k) was (5,0) and you have determined p is -1 input values and you are done

19. anonymous

would x =-1?

20. anonymous

isn'y y -1 @freckles

21. anonymous

isn't*

22. freckles

x and y are variables

23. freckles

you found (h,k) is (5,0) replace h with 5 replace k with 0 you found p=-1 replace p with -1

24. anonymous

what is x and y?

25. anonymous

god im so confused :|

26. anonymous

27. freckles

x and y are variables

28. freckles

can you replace h and k and p with what we have found?