SOLUTION: I need to graph y=x(1+x)^2 but i don know how to graph it at all could someone please help with steps on how to graph it completely,however read this thank you so much for the hel

Question 1099325: I need to graph y=x(1+x)^2 but i don know how to graph it at all could someone please help with steps on how to graph it completely,however read this thank you so much for the help it is much appreciated.
S,Wagner
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
You know the basic shape because it is a cubic polynomial; and since it is given in factored form, you can identify the zeros of -1 and 0. Want to find any max or min, maybe using derivative?

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Finding maximum or minimum values (as suggested by the other tutor) could help to solve some kinds of problems; but it won't help much for drawing a rough graph of the function.

With the function in factored form, you know the zeros are at x=0 and x=-1.
You also know that x = -1 is a double root; that means the graph will just touch the x-axis at that point instead of crossing it.
Finally since the leading coefficient is positive, you know the graph goes to negative infinity to the left and to positive infinity to the right.

So you know that, moving left to right, the function value...
starts large negative;
touches the x-axis at x=-1 but then stays negative;
passes through 0 at x=0; and
goes to positive infinity after x=0

Just that much will tell you the general behavior of the graph; you could plot a couple of additional points if you want a more accurate graph.
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