Question

the equation of a parabola is 12y=(x-1)^2-48. Identify the vertex focus and the directrix of the parabola

Answer 1

You still there?

Answer 2

yes

Answer 3

@legomyego180

Answer 4

this is the last question on my quiz i really need help

Answer 5

Are you familiar with vertex form?

Answer 6

uhh not really this is really confusing to me

Answer 7

It's ok. To find your vertex when the equation is written like this look at whatever x is being subtracted by. Can you tell what it is in this case?

Answer 8

1?

Answer 9

Keep in mind this only works when the equation is in this form:
\[y=(x-a)^2-c\]

where a and c are any number.

Yes, 1.

This means that the x-value of your vertex is one, so we have figured out half of it.

(1,y)

Still need to find the y value.

Any ideas on how to do that?

Answer 10

divide 12 y from each side?

Answer 11

Sure, you can do that. But if you have an x value, and you want to find its corresponding y vaule, you can just plug it back into the function. So plug x=1 into your function and see what you get for y. That will give you both points of your vertex. Does that make sense?

Answer 12

yes ok let me try that

Answer 13

i got 4

Answer 14

-4

Answer 15

oh ok i probably missed a step or something

Answer 16

so thats the vertex?

Answer 17

(1,-4) = vertex.

Keep in mind if this was something like (x+1) instead of (x-1) your x value for the vertex would be -1. Its whatever makes the thing inside the parentheeses zero.

Answer 18

ok got it

Answer 19

what about the rest

Answer 20

One sec. I havent done this in a while, so I'm learning this as I teach it

Answer 21

ok

Answer 22

https://www.youtube.com/watch?v=04nBaKx9wiM

Answer 23

I reccomend watching that all the way through.

Answer 24

ok thanks

Answer 25

So first thing lets rewrite
\[12y=(x-1)^2-48\]
as
\[y+48=\frac{ 1 }{ 12 }(x-1)^2\]

because w want to get the x^2 value by itself.

Answer 26

Actually, that should just be \[12y+48=(x-1)^2\]

Answer 27

Then:
4P=12

P=3

So add 3 to your vertex's y value to get your Focus, and subtract P to get your directrix.

Sorry, im kind of lousy at this stuff

Answer 28

But it is the correct answer.

Answer 29

thanks its ok!