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

- anonymous

- chestercat

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- freckles

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

- freckles

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

- anonymous

(0,5)?

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## More answers

- freckles

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

- anonymous

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

- freckles

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

- 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 :/

- 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)

- freckles

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

- anonymous

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

- freckles

right

- freckles

the vertex is (5,0)

- anonymous

what do i do with that?

- anonymous

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

- freckles

|dw:1438724452936:dw|

- anonymous

so (5,-1)?

- 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
\[(x-h)^2=4p(y-k) \\ \text{ divide } 4p \text{ on both sides } \frac{1}{4p}(x-h)^2=y-k \\ \text{ add } k \text{ on both sides } \\ y=\frac{1}{4p}(x-h)^2+k\]

- 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

- anonymous

would x =-1?

- anonymous

isn'y y -1 @freckles

- anonymous

isn't*

- freckles

x and y are variables

- freckles

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

- anonymous

what is x and y?

- anonymous

god im so confused :|

- anonymous

or nahh XD im dead

- freckles

x and y are variables

- freckles

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

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