Question

What quadratic function is formed with a directrix of y=-2 and a focus of (1, 6)?

Answer 1

see the vertex must be exactly between focus and directrix i.e 1 and -2

Answer 2

eh nvm, Ur directrix is y = -2 , so it wud be between, 6 and -2

Answer 3

How would I turn that into a function?

Answer 4

function wud be (x-h)^2 = 4(a)(x-k)^2

Answer 5

where h and k are coordinates of vertex

Answer 6

*(x-h)^2 = 4 (a) (y-k)^2 it shud be, nevermind the typo

Answer 7

I'm really confused. :/

Answer 8

thats the equation of parabola , even i m confused over how to find the values of vertex :S ,once we get the value of vertex, we can find it

Answer 9

give me a minute

Answer 10

okay. .-.

Answer 11

ok as the directrix is y = -2 and focus is (1,6) , the vertex must be midway between these two

Answer 12

that is (1,2)

Answer 13

got it so far?

Answer 14

I think so.

Answer 15

ok now equation of parabola with vertex(h,k) i.e. (1,2) in our case is (y-h)^2 = 4a(x-k)^2
where a is distance between vertex and directrix

Answer 16

that makes our equation (y-2)^2 = 4a(x-1) ^2

Answer 17

all clear so far?

Answer 18

It needs to be in the y= form though o:

Answer 19

whats a quadratic equation?

Answer 20

we can solve it and get it in y = x^2 + constant form

Answer 21

Ohh

Answer 22

got it?

Answer 23

I think so.

Answer 24

rite ,then lets find a , i.e. distance between vertex and directrix, and how wud we do that?

Answer 25

So the vertex is 1,2 and the directrix is 0, -2?

Answer 26

yerr

Answer 27

is the distance sqrt(17)?

Answer 28

rite , approx 4 then

Answer 29

(y-2)^2 = 4a(x-1) lets use this equation now

Answer 30

Would the answer to my question by any chance be f(x)=1/8(x-1)^2-2?

Answer 31

ehh i guess i messed up with the parabola equation

Answer 32

Now I'm confused.. again xD

Answer 33

no, its correct lol

Answer 34

Is that the right answer? o.o

Answer 35

wait lemme solve

Answer 36

or would it be f(x)=-1/8(x+1)^2-2? o.o

Answer 37

the equation shud be (x-1)^2 = 4(y-2)

Answer 38

thats where i messed up

Answer 39

x^2+1-2x = 4x4(y-8)

Answer 40

ah why did i oopen it, We just need to find the y lol

Answer 41

wait wait. would this be a parabola that's got a smile or a frown? xD (i don't remember the exact word for it.. oops.)

Answer 42

see the vertex 's coordinates

Answer 43

they are (1,2)

Answer 44

f(x)=1/16(x-1)^2+2 has a vertex of 1,2 o:

Answer 45

now can ya tell? :P

Answer 46

would it be f(x)=1/16(x-1)^2+2? o.o

Answer 47

yes, !!

Answer 48

:DD yaya! thank you!

Answer 49

if they got same vertex, means both are same parabolas

Answer 50

rite, DOne! lol sorry took me time to recall all the geometry things, havent studied it in a while

Answer 51

it's fine. xD thanks though! :)

Answer 52

you're welcome :)