The function y=(x+1)(x-2)(x-4) cuts x-axis (i.e. the line y=0) at three points,
Where x+1=0 or x=-1 and
x-2=0 or x=2 and at x-4=0 or x=4
Now, these three points (-1,0), (2,0 and (4,0) divide x-axis in four parts
(1) In segment x<-1, all the three terms of y are negative and hence product is negative and the curve is below x-axis.
(2) In segment -1 < x < 2, while first term is positive, other two terms are negative. Hence product is positive and the curve is above x-axis. Note that it crossed x-axis at x=-1.
(3) In segment 2 < x < 4 while first two terms are positive, the third term is negative, hence product is negative and the curve is below x-axis. Note that it crossed x-axis at x=2.
(4) In segment x>4 all the terms are positive, hence product is positive and the curve is above x-axis. Note that it crossed x-axis at x=4.
One can also put some other values of x now in different segments and complete the graph.
It appears as shown below.
graph{(x+1)(x-2)(x-4) [-20, 20, -10, 10]}
