Question 932817
{{{f(x)=2x(x^2-x-20)}}} 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.



{{{f(x)=2x(x+4)(x-5)}}}, the function in completely factored form.




INTERVAL_________________________SIGN of f
{{{x<-4}}}_________________(-)(-)(-), NEGATIVE
{{{-4<x<0}}}_______________(-)(+)(-), POSITIVE
{{{0<x<5}}}________________(+)(+)(-), NEGATIVE
{{{x>5}}}__________________(+)(+)(+), POSITIVE


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