Make tables of values for the two graphs from -2 to 6.

y=3x(4-x)          y=5(x-2)
x | y              x| y
-2|-36            -2|-20 
-1|-15            -1|-15
 0|  0             0|-10
 1|  9             1| -5 
 2| 12             2|  0
 3|  9             3|  5
 4|  0             4| 10
 5|-15             5| 15
 6|-36             6| 20

Plot the points.  The graph below does not contain all the points, but it is
to scale. Each block is 1  cm on the x-axis to 5 cm on the y-axis, but you will
need to extend the graph to be able to show the first and last points on the
tables of values. 


From the graph we can deduce the maximum value of the equation y=3x(4-x),
the red graph, is 12 for the point (2,12) is the highest point, and we can
deduce that the roots of the equation y=3x(4-x) are 0 and 4 for those are
the values on the x-axis where the red graph crosses the x-axis.

We can also show that the roots of y=3x(4-x) are 0 and 4 using algebra
instead of deducing them from the graph. We do that by setting y=0 and
solving for x:

y = 3x(4-x)
0 = 3x(4-x)
Divide both sides by 3
0/3 = x(4-x)2
0 = 4x-x2
4x-x2 = 0
Factor out x
x(4-x) = 0
x=0; 4-x=0
      -x=-4
       x=4

Edwin