Question 1210454
Draw the graph of y = 3x(4- x ) for value of x ranging from-2 to 6 on the same
axes draw the line y=5(x-2) use a scale of 1 cm to 1 unit on the x axis and 1cm
to 5 unit on the y axis.From your graph find the roots of equations 3x(4-x)
write down the maximum value of y=3x(4-x) and deduce the root of the equation.
<pre>
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. 
{{{drawing(230,230,-2,6,-15,25,graph(230,230,-2,6,-15,25,3*x*(4-x),5*(x-2)),

circle(-1,-15,.12),grid(1),
circle(0,0,.12),
circle(1,9,.12),
circle(2,12,.12),
circle(3,9,.12),
circle(4,0,.12),
circle(5,-15,.12),

circle(-2,-20,.12),
circle(-1,-15,.12),
circle( 0,-10,.12),
circle( 1,-5,.12),
circle( 2,-0,.12),
circle( 3,5,.12),
circle( 4,10,.12),
circle( 5,15,.12),
circle( 6,20,.12)

)}}}

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)<sup>2</sup>
0 = 4x-x<sup>2</sup>
4x-x<sup>2</sup> = 0
Factor out x
x(4-x) = 0
x=0; 4-x=0
      -x=-4
       x=4

Edwin</pre>