SOLUTION: The equation is f(x)=2x^3-2x^2-40x. I understand that you make this equal to 0. Then you would get X=0, x=-4, x=5. But I don't understand how you get the table to graph the rest. A

Question 932817: The equation is f(x)=2x^3-2x^2-40x. I understand that you make this equal to 0. Then you would get X=0, x=-4, x=5. But I don't understand how you get the table to graph the rest. And how would you write the result?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The equation is f(x)=2x^3-2x^2-40x. I understand that you make this equal to 0. Then you would get X=0, x=-4, x=5. But I don't understand how you get the table to graph the rest. And how would you write the result?
------------
Use y = 2x^3-2x^2-40x
Pick values for x and find y. That's the table.
You can use Excel to do that.
---
Plot the (x,y) points and draw a curve thru them.
That's the graph.

Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
and the roots are 0, -4, 5. The roots are the x values where the function f either touches or crosses the x-axis. The roots cut the x-axis into four intervals on which you can test the sign of f in each interval. You can simply pick an x value in each interval, and check the resulting sign for f.

, the function in completely factored form.

INTERVAL_________________________SIGN of f
_________________(-)(-)(-), NEGATIVE
_______________(-)(+)(-), POSITIVE
________________(+)(+)(-), NEGATIVE
__________________(+)(+)(+), POSITIVE

This table indicates the graph of f(x) CROSSING the x-axis at every root. This helps in forming the graph.
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