Parabolas (1 Viewer)

[Boonyak]

Hey guys i need to remember how sketching parabolas works like x^2-1 is one down etc like when is it to the right 1 up and stuff cheers. and how do i sketch something thats in terms of x for eg x=y^3

Thanks in advanced

 

[deswa1]

With a lot of these, the easiest way is to graph the original function and then test a few points. For example, with y=x^2-1, it is clear that for every value of x, y=x^2-1 will be one less than y=x^2. Therefore you just shift the graph down one unit. When you do a few of them, you will be able to tell the translation very quickly...

To sketch something like x=y^3, note that it is the same thing as y=x^(1/3) so you can just sketch that.

 

[Timske]

are you learning inverse boonyak?

 

[RealiseNothing]

Pretty sure you can just sketch y = x^3 then rotate it 90 degress clockwise.

 

[SpiralFlex]

Inverse functiiiiiiooooooonnnnnnnn

 

[IamBread]

Inverse function

 

[bleakarcher]

just reflect y=x^3 about the line y=x to obtain the graph of y=x^(1/3).

 

[SpiralFlex]

Note: This is posted in 2U though. They don't do inverses.

 

[Boonyak]

Thanks spiral lol was stressing say wtf is inverse ehehe .

 

[Timske]

ohhh yeaaah......

 

[SpiralFlex]

Some notable things, but nothing else you really need to know about this graph. Just note:

- As x values get larger, the corresponding ordinates get larger.

- Similarly as x values get smaller, the corresponding ordinates get smaller.

- There is a vertical tangent at x = 0. (This is beyond the scope of 2U)

But in 2U maths, we have found that for stationary points, the tangents will be parallel to the x axis. Hence horizontal. (Gradient 0)

What if we could find vertical tangents? Well we know a straight line parallel to the y axis has an undefined gradient, so dy/dx=undefined.





For vertical tangents, y'=undefined.



When ,

Hence there is a vertical tangent at the origin.


Now, if you were to draw this, it will be flat near the origin then diverge out very quickly! Have a go at graphing it!

 

[Carrotsticks]

Now, if you were to draw this, it will be flat near the origin then diverge out very quickly!

Are you sure about this part?

 

[nahi11]

If ever in doubt just test a few points. It can save you a few marks. After testing about three points you should be able to sketch the graph.

EDIT: How do you guys change from normal text to the 'natural math' text? ie what Spiral has done in the post above me.