Cubic Graphs (2 Viewers)

[hholbrook]

Hi,

I keep having the same problem with cubic graphs. For some reason my y intercept is (sometimes, not always) the reverse of what it should be e.g. instead of getting 12, I get -12. One of the questions was:

y=-2(x-3)(x-1)(x+2)

I had my y intercept as -12 but it should be 12. This problem has been occurring quite often. Any help is appreciated.

Thank you!

 

[deswa1]

Hi,

I keep having the same problem with cubic graphs. For some reason my y intercept is (sometimes, not always) the reverse of what it should be e.g. instead of getting 12, I get -12. One of the questions was:

y=-2(x-3)(x-1)(x+2)

I had my y intercept as -12 but it should be 12. This problem has been occurring quite often. Any help is appreciated.

Thank you!

For this question, the y intercept is -12. You sub in x=0 and you get y=-2(-3)(-1)(2)=-12 so you are right lol

 

[hholbrook]

well thats what I thought but the book has 12 with it running through 1, -2, and -3. The book must be wrong.

 

[Fawun]

y = (0-3) x (0-1) x (0+2)

-3 x -1 x 2 = 6

6 x -2 = -12

I got -12 as well.

 

[Demento1]

A textbook is not always correct.

 

[Carrotsticks]

Normally, it would be 12. However, since we have a negative cubic polynomial, it is now -12.

 

[hholbrook]

Thanks carrotsticks. What is a negative cubic polynomial exactly?

 

[deswa1]

Thanks carrotsticks. What is a negative cubic polynomial exactly?

When the leading coefficient is negative. For example, consider f(x)=-x^3+6x^2-2x+6. Basically, the curve starts from below the x axis not above it like in a positive cubic (because the limit x-> infinity is negative infinity)

 

[Carrotsticks]

It is a cubic polynomial, which has limit infinity as x -> - infinity, and limit -infinity as x -> +infinity.

 

[hholbrook]

Sorry I don't understand. Could you explain in basic terms?

 

[Shadowdude]

draw the graph

as you go more to the left, does it go up the page?
and as you go more to the right, does it go down the page?

if so, you have a negative cubic

 

[hholbrook]

So how do I identify if it is a negative or a positive cubic?

 

[kev-kun]

Well from a visual standpoint, generally most positive cubics appear as
As for negatives they are a reflection type thingy of the positive slope
Hope that helps??