C1 Graphs help?

I'm drawing graphs, and there are two equations:

1) y = x (x + 1) (x - 1)
2) y = x (x + 1 ) (1 - x)

They both give the same points where it crosses the x axis (0,0) (-1,0) and (1,0) however the answers say that the graphs are different in the way the graph actually goes through the points. Here's a picture to show what I mean

ImageUploadedByStudent Room1365014692.721639.jpg

ImageUploadedByStudent Room1365014692.721639.jpg

It's a poor quality picture, sorry! Anyway, my question is, how do I determine how the line going through the points goes? Because as seen in the two diagrams in the image, they're kind of mirror images of each other and I don't get where that comes from.

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Reply 1

Indeterminate

Original post by JodieW

Yes, but the (1-x) throws a twist into the tale. Can you see why? If not, expand the brackets :smile:

Reply 2

JodieW

Original post by Indeterminate

Yes, but the (1-x) throws a twist into the tale. Can you see why? If not, expand the brackets :smile:

Oh okay, so the second one was the negative of the first one, so is it because it has that negative sign that the line of the graph goes in that direction?

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Reply 3

Indeterminate

Original post by JodieW

Oh okay, so the second one was the negative of the first one, so is it because it has that negative sign that the line of the graph goes in that direction?

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Yep, multiplication by a negative flips it the other way up :smile:

Reply 4

JodieW

Original post by Indeterminate

Yep, multiplication by a negative flips it the other way up :smile:

Oh I see, thanks! :smile:

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Reply 5

JodieW

Original post by Indeterminate

Yep, multiplication by a negative flips it the other way up :smile:

Hey, sorry to bother you again, but I'm having another issue with graphs :smile:

Say I have an x^3 graph that goes through (0,0) and (1,0), how do I know whether to draw it like this:

ImageUploadedByStudent Room1365113936.567801.jpg

Or this:

ImageUploadedByStudent Room1365113978.372494.jpg

It really confuses me, is there something I don't know that tells me whether or not the graph touches the point or actually goes through it? The curve is y = x (x - 1)^2 by the way. Could you help me please? :smile:

Thank you!

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Reply 6

Indeterminate

Original post by JodieW

Hey, sorry to bother you again, but I'm having another issue with graphs :smile:

Say I have an x^3 graph that goes through (0,0) and (1,0), how do I know whether to draw it like this:

ImageUploadedByStudent Room1365113936.567801.jpg

Or this:

Thank you!

Posted from TSR Mobile

Well, a graph touches the x axis at a point if it has a double (or higher) root there.

So

f(x)=x^2(x-1)

would touch the x axis at x=0, but then would go through x=1 as normal.

So what can you say about your graph? :smile:

(edited 11 years ago)

Reply 7

2710

Original post by JodieW

Hey, sorry to bother you again, but I'm having another issue with graphs :smile:

Say I have an x^3 graph that goes through (0,0) and (1,0), how do I know whether to draw it like this:

ImageUploadedByStudent Room1365113936.567801.jpg

Or this: