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# C1 Graphs help? watch

1. 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

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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2. (Original post by JodieW)
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

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.

Posted from TSR Mobile
Yes, but the (1-x) throws a twist into the tale. Can you see why? If not, expand the brackets
3. (Original post by Indeterminate)
Yes, but the (1-x) throws a twist into the tale. Can you see why? If not, expand the brackets
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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4. (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
5. (Original post by Indeterminate)
Yep, multiplication by a negative flips it the other way up
Oh I see, thanks!

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6. (Original post by Indeterminate)
Yep, multiplication by a negative flips it the other way up
Hey, sorry to bother you again, but I'm having another issue with graphs

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:

Or this:

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? Thank you!

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7. (Original post by JodieW)
Hey, sorry to bother you again, but I'm having another issue with graphs

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:

Or this:

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? 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

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

8. (Original post by JodieW)
Hey, sorry to bother you again, but I'm having another issue with graphs

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:

Or this:

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? Thank you!

Posted from TSR Mobile
You can just stick in x = 1/2 and see what the y value is. Although you should understand why it is like that, with the post above
9. (Original post by Indeterminate)
Well, a graph touches the x axis at a point if it has a double (or higher) root there.

So

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

Is it that simple? Thanks, I'm relieved that I finally know now haha

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