Question

I need help with parabolas!

Answer 1

I can probably help

Answer 2

\[y=\frac{ 1 }{ 32 }X ^{2}\]

Answer 3

Im working on conic sections

Answer 4

Are you wondering what it'll look like? This will just stretch the function x^2.. See attached

Answer 5

I need to be able to graph it @dc104

Answer 6

On graph paper, or a sketch? If it's a sketch it's going to look just like x^2 since all that is changing is the graph is being stretched by a scale factor of 32

Answer 7

This is what I got, I have to find the directix, and the focus the plug in X in the equation the I put up earlier

Answer 8

@dc104

Answer 9

@KirbyLegs could you possible help me with this

Answer 10

your parabola looks ill (tipped over). It should look like a smile

Answer 11

In my lesson it had given me an example in which it opened to the left. But I see since this is a horizontal directix it should either open up or down

Answer 12

You should match your parabola to
\[ y= \frac{1}{4p} x^2 \]
p is the distance from the vertex to the focus, and (in the other direction) the distance from the vertex to the directrix.

the vertex (the bottom of the parabola) is at (0,0) for your parabola

Answer 13

It looks like you figured out p is 8 (and got the correct directrix.)
the focus should be 8 up from (0,0)

Answer 14

I get up to breaking down the equation as in doing \[y=\frac{ 4 }{ 4(8)}x ^{2}\]

Answer 15

Then P is that 8 and I think that's where I start getting confused

Answer 16

you mean
\[ y=\frac{ 1 }{ 4(8)}x ^{2} \]
there is no 4 "up top" in the fraction

Answer 17

oops sorry it was a typo I didn't catch

Answer 18

when you have y= x^2 that is a smile
y = -x^2 is a frown
x = y^2 is sideways (like your picture)

it should be clear that when y = 1/32 x*x
that y can not be minus (because x*x will always be 0 or bigger... example: x= -1 causes y= 1/32 * -1* -1 = 1/32 which is bigger than 0)

that is the long way of saying y is always plus, and you will get a U shape

Answer 19

I understand where I went wrong with where it faced, I just have no Idea how I get it the right way

Answer 20

the vertex will be at x=0 (and y= 1/32 * 0 = 0)
the directrix will be 8 below (0,0) just where you put it.
the focus will be 8 above (0,0)

to finish the plot, notice when x= 4, y= 1/32 *4*4= 16/32= 0.5
plot (4, 0.5)
also, when x=-4 you will also get y=0.5. plot (-4,0.5)

Answer 21

I just have no Idea how I get it the right way

Don't draw it that way?

so far you have 3 points:
(-4, 0.5), (0,0), (4, 0.5)

Answer 22

Can you plot those 3 points?

Answer 23

okay I did

Answer 24

you can figure out two more points. if x is 6 (or -6) what is y ?

Answer 25

1.125?

Answer 26

and I also a focus point how do I find that

Answer 27

the focus is 8 up from (0,0)

Answer 28

Right, I had just found it. Because when the directix is horizontal the focus is (0,p)

Answer 29

You should have enough points to sketch in the (very flat) parabola.

Answer 30

and this one goes down, correct?

Answer 31

its goes up, never mind on that one

Answer 32

You should get something like this

Answer 33

Would that be counted as correct in your book?

Answer 34

I though you figured out y = 1.125 when x is 6 (or -6)
your line is up at y=3 when x is 6. It goes up too fast.

Answer 35

I would put a point at x=10 (y will be 10*10/32 = 100/32 or 3.125)
and the same at x=-10
then connect the dots...

Answer 36

better, but read my last post.

Answer 37

how did you even get that X=6 and -6
When I was in my lesson I couldn't figure that one out either

Answer 38

the parabola will be at some y when x is 6. How do we find y?
we use
y = 1/32 * x^2

I picked 6 because I want some points to plot. We could pick x= 1,2,3,4... but we can get away with just a few x values ... say at x=0 , 4, 6, 10

Answer 39

Oh, so you can choose any reasonable X value

Answer 40

If you look at your plot, at every x you can see the parabola has some y value. The idea is that the graph matches the numbers from y= 1/32 x^2

A computer would figure out y for x every tiny step (0, 0.001, 0.002, all the way up to x=10) and draw a zillion points that would be so close it would look like a line.

Answer 41

can you plot the points for x=10
(and x=-10)

Answer 42

What did you use for your graph, that graphing thing was provided to me from my teacher, anything better would be great

Answer 43

http://www.geogebra.org/cms/en/
would plot it automatically (but you should learn how to do it by hand, just so you know how to do it)

Answer 44

A plus

Answer 45

Awesome! Thank you so much, and thank you for taking your time with me. Not very many people will do that!

Answer 46

yw