## anonymous one year ago Cubic help

1. anonymous

Graph doesn't look very cubic to me though which makes me thing I did it wrong.

2. anonymous

what's the exact question?

3. anonymous

as in what is the exact wording of the question you're trying to answer. positive rate of change → function is increasing negative rate of change → function is decreasing

4. mathmate

Is it possible to post an image of the original question? That's the fastest way to get help!

5. anonymous

You're giving a lot of information, but there's no context

6. anonymous

So I can do cubic regression or do l*w*h where (12-x) represents the sides and (x) represents the height of the boxes... whichever one you guys are able to help me with.

7. anonymous

Kinda wanted to know how to do it by hand, but maybe that isn't good to know as a pre-algebra student.

8. mathmate

Hints: "where (12-x) represents the sides and (x) represents the height of the box)" means: So if the height (x)=1, then the sides are (12-1)=11, or 1*11*11, V=121 If height is 2, sides are 12-2=10, volume = 2*10*10=200 in general, if the height equals x, the volume is x(12-x)(12-x), which is evidently a cubic. Do you agree with the above calculations?

9. anonymous

Yeah that makes sense.

10. mathmate

Yes, a cubic is a polynomial, which is any expression in the form of "the sum of positive integer powers of a variable, each multiplied by a constant".

11. mathmate

I do not know how you got y=-12x^2 + 49.6x + 67.2 but the volume itself is already a cubic (third degree polynomial), and will not need to have a cubic regression, because it is exactly a cubic polynomial.

12. mathmate

But your table does not correspond to the given constraints of x=height, (12-x)=sides, so it cannot be used to "generate" your regression cubic.

13. mathmate

But your table does not correspond to the given constraints of x=height, (12-x)=sides, so it cannot be used to "generate" your regression cubic that represent the results of the problem.

14. anonymous

But if it's wrong then I will just go with the way you showed me.

15. mathmate

In your table, I do not understand what you meant by "size of corner cut ". I use x=height, as per instructions.

16. anonymous

size of corner cut meants (remember I used grid paper to make cubes) I had to cut off one square on each corner. Let me draw it for you okay. I'm really sorry for confusing you. I did a very bad job explaining everything.

17. anonymous

Give me a few minutes. please.

18. mathmate

So that means the height. |dw:1440381788262:dw|

19. anonymous

right but in the first drawing it's 10 by 10

20. mathmate

So you need to make a table: |dw:1440381900195:dw|

21. mathmate

Can you please look at my table and see if you agree with it?

22. anonymous

for that table you draw for 3 would be 12-3 = 9 3*9*9 or 243

23. mathmate

exactly!

24. anonymous

Yeah that makes sense to me.

25. anonymous

So was my equation wrong then? I can't get an equation from your table you drew right?

26. mathmate

So use this new table and try to fit a cubic and see what you get. "Our" volume is x(x-2)^2=x^3-24x^2+144x. Your "regression" cubic should give exactly the same expression.

27. mathmate

Remember to fit a cubic you need at least 4 points, and preferably more if you're doing regression.

28. anonymous

wait what do I put in for x?

29. anonymous

Are you there @mathmate

30. mathmate

Sorry, I was afk. a bunch of numbers, like 1,2,3,4,5,6, or 2,4,6,8,10, ... If everything is calculated correctly, they should all give the same cubic polynomial.

31. mathmate

The numbers don't have to be evenly spaced like my examples, they could be x=1,2,5,10,21 if you want.

32. mathmate

Oops, cannot be greater than 12! So forget the 21!

33. anonymous

I graphed this on my paper I did my y axis by 10's and my x axis 12345 but skipped every two lines

34. anonymous

not sure if that's relevant

35. mathmate

Trick to graphing by hand is to get the smallest and largest y to start. So start with the table. |dw:1440383506458:dw| so make a y-scale high enough for 256, and x from 1 to 10.

36. anonymous

okay.

37. anonymous

okay thanks for your help. Really appreciate you sitting here and going over this with me :)))

38. mathmate

No problem! :)