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# How do you know when a Cubic graph is positive? watch

1. I have the graph y = (x+1)(x+3)^2.

I know that it is a cubic, but how do I distinguish whether it's a negative or positive one?

Thanks.
2. it is a negative if the coefficient of x^3 is negative. Expand it and find out if it is.
3. (Original post by Alex-Torres)
I have the graph y = (x+1)(x+3)^2.

I know that it is a cubic, but how do I distinguish whether it's a negative or positive one?

Thanks.
Determine the max and min points through (dy/dx)
Then you will be able to see the direction the curve is moving ^_^

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4. (Original post by Namige)
it is a negative if the coefficient of x^3 is negative. Expand it and find out if it is.
(Original post by Appleblossom95)
Determine the max and min points through (dy/dx)
Then you will be able to see the direction the curve is moving ^_^

This was posted from The Student Room's iPhone/iPad App
Thanks!
5. A more rough-and-ready way: you know the roots are at -1 and -3, so just shove in x=-4 (which is, for these purposes, "infinity"; any point westwards of -3 would do); you get -3*(-1)^2 = -3, which is negative, so it's being sent towards negative infinity as x gets more negative.
6. Smaug123's way is good but I got a little confused with it myself and had to think through his wording. Instead of picking -4, I would pick anything greater than -1, say +1. Plugging this in gives us a positive answer and you see that as x goes towards plus infinity, the graph is increasing. The reason I think (for me) this is better is that when you think of positive or negative cubic graphs, you look at the "final line" (i.e the bit after the second turning point as ) of the cubic and see if that is increasing (which means positive) or decreasing (negative). With Smaug's way, he has just done it the other way round and even though that gives you the right answer, you are kind of looking backwards at it.

The most obvious way, if you have the function is to see if it starts with or . Seeing as your one is factorised, you need to expand to see if the coefficient of is positive of negative. Firstly, we see that the first root is (x + 1), which has a positive coefficient for x. Now as the second one is x + something squared, you know that the x coefficient will be positive as we will either have or (like we do in this case) . Now as you have two positives, you know the positive times positive = positive and so your coefficient of will be positive.

In other words, instead of having to expand the whole thing, look at the coefficients of 'x'. If one or all of them are negative, then your cubic is negative. If one or all of them are positive, then your cubic is positive. Why?

- negative * positive * positive = negative * positive = negative,
- negative * negative * negative = negative * positive = negative.
- negative * negative * positive = positive * positive = positive,
- positive * positive * positive = positive * positive = positive.
7. (Original post by claret_n_blue)
Instead of picking -4, I would pick anything greater and -1, say +1.
Yep, in hindsight that's much easier

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