SOLUTION: Figuring out graphing of this polynomial: f(x) = 12x^3 - 12x^2 - 24x what I have so far: I know I can factor it down, therefore 12x(x+1)(x-2) and the x-int would be (-1,0

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Question 916845: Figuring out graphing of this polynomial:
f(x) = 12x^3 - 12x^2 - 24x

what I have so far:
I know I can factor it down, therefore 12x(x+1)(x-2)
and the x-int would be (-1,0),(2,0)
But why is (0,0) also a factor? I don't understand that.

also how would I find the degree and leading coefficient? very lost on that concept
And when I plug this poly into a graphing calculator it has a steepness and a lowness at two points. I am in precalculus so I don't know the finer details of graphing/derivatives and I must be able to do this freehand how would I know how far up to make the graph and how far low to make the graph? Am I just suppose to estimate them for precalculus? What if both sides bounces how do I tell which one is higher or lower or if they are both the same?

Thank you
Answer by josgarithmetic(39615) (Show Source):
You can put this solution on YOUR website!
You also have another x-intercept: (0,0), because of the factor, x.

The highest exponent of the variable is 3, from 12x^3.
The degree of the function is 3.

You can test the intervals which the x-intercepts define and get the signs in each interval. The intervals to check are these:
,
;
;
.

Finding the maximum and minimum values is something that you just must estimate, if you want these. Beginning Calculus will teach how to determine them more accurately.

Based on the leading term of f, the values of f fall toward the left and rise to the right.