Hey @amistre64 :). Find the equation of the parabola with a vertex of (-1,2) and a focus of (-1,0)

- Lukecrayonz

Hey @amistre64 :). Find the equation of the parabola with a vertex of (-1,2) and a focus of (-1,0)

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- amistre64

the distance from vertex to focus is imporant to know

- Lukecrayonz

That's all that is given..

- Lukecrayonz

Here's an example: http://screensnapr.com/v/LLWoVz.png

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- amistre64

|dw:1332548394602:dw|

- amistre64

you need to find the distance from the focus to the vertex with what is given

- amistre64

how would you find the distance between 2 given points?

- Lukecrayonz

d=xqrt(x2-x1)^2+(y2-y1)^2

- Lukecrayonz

sqrt* sorry.

- Lukecrayonz

So sqrt(-1+1)+(0-2), sqrt(-2), isqrt(2)

- amistre64

you need to practice your formula :) you should end up with a distance of 2

- Lukecrayonz

o.O Where did i go wrong?

- Lukecrayonz

oh. wow, i see

- amistre64

square your sums

- Lukecrayonz

i didnt square the answers haha

- Lukecrayonz

okay, so its -2^2, 4, sqrt(4)=2.

- amistre64

good
now, the formula for a parabola in geometry is given as: 4ax = y^2 and there are 4 different versions of it depending on how the parabola works; but "a" is our distance from vertex to focus

- amistre64

so, we know this opens up towards the focus; which is situated below the vertex

- Lukecrayonz

I'm trying to do this based off the example, but its so strange..

- Lukecrayonz

http://screensnapr.com/v/ZX62B4.png

- amistre64

the example is using this format as well; but lets get the parabola oriented correctly, then we will move it to the correct vertex point

- amistre64

|dw:1332548943087:dw|

- Lukecrayonz

And the distance between them is two, since we solved for that, and p=2.

- amistre64

-x^2 = 4ay will set this up good; and a = 2

- amistre64

-x^2 = 8y yes

- Lukecrayonz

Oh, you do -x^2=4ay, my online book does p for a.

- amistre64

right

- Lukecrayonz

Okay, so our equation according to my book, is (x-h)^2=4p(y-k)

- amistre64

now that we have the parabola set up at the origin, we can move it to the given vertex

- Lukecrayonz

Since p is greater than zero, and it opens up.

- Lukecrayonz

Sorry, opens down haha, (x-h)^2=4p(y-k)

- amistre64

p measures distance at the moment, so it aint negative

- amistre64

the vector from v to f would give us distance and direction

- amistre64

so, if you want to keep in mind that f-v = distance and direction from v to f; then we can assign a sign to p

- Lukecrayonz

Didn't we solve for p though..?

- amistre64

we solved for the distance measured by p; but without specifying a direction in our workings, we cannot verify its direction (+ or -)

- amistre64

in other words, we have |p|

- Lukecrayonz

Makes sense, so what do we do from here?

- amistre64

a picture tells us the the parabola will open down; so if anything the distance and direction of p = -2, as long as we keep in mind that this is the vector from v to f, and not from v to d(the directix)

- amistre64

x^2 = 4(-2)y -> x^2=-8y
now we "move" this parabola from the origin, to the given vertex point

- amistre64

(x-vx)^2 = -8(y-vy)

- Lukecrayonz

(-1,2)

- Lukecrayonz

y=-(1/8)(x+1)^2+2

- amistre64

yes, if we wnat this to look like a "usual" parabola equation

- Lukecrayonz

Just looked up the answer, wondering how they gt to there.

- Lukecrayonz

got*

- Lukecrayonz

"The distance between the vertex and the focus is p.
p = sqrt [ ((-1+1)^2 +(2-0)^2] = sqrt(4) = 2
The focus lies below the vertex, so p=-2 and the parabola slopes downward.
The vertex and focus lie on the line x=-1 which is vertical
Therefore, the parabola is of the form (x-h)^2 = 4p(y-k) , (h,k) being the vertx
(x+1)^2 = 4p(y-2)
(x+1)^2=-8(y-2)
y-2 = (-1/8) (x+1)^2
y = (-1/8)(x+1)^2 + 2"

- amistre64

that would be a good path to follow :)

- Lukecrayonz

Got it :D

- Lukecrayonz

Dont know why, this is one problem when you explained it, it actually got more complicating, haha. Usually I get it right away once you do it.

- amistre64

:) i blame the fall of rome

- Lukecrayonz

NOOOOOOOOOOOOOOOOOO, A WORD PROBLEM!

- Lukecrayonz

I BLAME THE CREATORS OF CALCULUS :'(

- Lukecrayonz

I'll make a new question..

Looking for something else?

Not the answer you are looking for? Search for more explanations.