Question

hi my name is jennifer







and i need YOUR help?❤️ medal rewarded❤️
http://assets.openstudy.com/updates/attachments/53b36d15e4b02cb280b799b7-jenniferjuice-1404267832452-flvs.png

Answer 1

@satellite73

Answer 2

My name is Sammi ;p

Answer 3

lol well sammi can you please help me?

Answer 4

another?

Answer 5

we can do this one too

Answer 6

medal for your unique way of asking lol

Answer 7

really takes only two steps
focus is at \((2,4)\) directrix is \(y=8\) what is the vertex? hint: it is halfway between the focus and the directrix

Answer 8

@ikram002p well thank you :P

Answer 9

@satellite73 okay so

Answer 10

i am asking
what is half way between \((2,4)\) and \(y=8\) or if it is easier, what is half way between \((2,4)\) and \((2,8)\)
or even "what is half way between \(4\) and \(8\) ?"

Answer 11

4

Answer 12

no four is not half way between 4 and 8

Answer 13

how about this
what is the average of 4 and 8 ?

Answer 14

Average of two numbers is sum of the two numbers divided by two.
Average of three numbers is sum of the three numbers divided by three.
...etc.

Answer 15

is it 6? @satellite73 @mosaic

Answer 16

HELP?!?!?!!

Answer 17

Yes, 6 is half way between 4 and 8.
Therefore, the vertex which is half way between (2,4) and (2,8) is: ?

Answer 18

im sorry idk ._.

Answer 19

wait what im seriously lost right now

Answer 20

why did everyone leave noo please help me :(((

Answer 21

Focus is at (2,4)
Directrix is y = 8
Vertex is half way between focus and directrix and is at (2,6).

Equation of parabola in vertex form is y = a(x-h)^2 + k ---- (1)
where (h,k) is the vertex and |a| = 1/(4p) where p is the distance between vertex and focus. Here, p is the distance between (2,4) and (2,6) and is 2.
|a| = 1/(4p) = 1/(4*2) = 1/8
Since the vertex is below the directrix, the parabola opens downwards which means 'a' has to be negative. So a = -1/8.
h = 2, k = 6

Plug a,h,k into (1)

Answer 22

I find the following method a bit easier for me:
The parabola has the property that ANY point (x,y) on the parabola will be equidistant from the focus and the directrix. That is, \( (x-2)^2 + (y-4)^2 = (y-8)^2 \). Simplify.

\( (x-2)^2 = (y-8)^2 - (y-4)^2 = (y-8+y-4)(y-8-y+4) = \\
(2y-12)(-4) = 2(y-6)(-4) = -8(y-6) \\
y = -\frac 18(x-2)^2 + 6\)