document.write( "Question 1210454: Draw the graph of y = 3x(4- x ) for value of x ranging from-2 to 6 on the same
\n" ); document.write( "axes draw the line y=5(x-2) use a scale of 1 cm to 1 unit on the x axis and 1cm
\n" ); document.write( "to 5 unit on the y axis.From your graph find the roots of the equation
\n" ); document.write( "y=3x(4-x), write down the maximum value of y=3x(4-x) and deduce the root of the equation. \n" ); document.write( "
Algebra.Com's Answer #852636 by Edwin McCravy(20077)\"\" \"About 
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Draw the graph of y = 3x(4- x ) for value of x ranging from-2 to 6 on the same
\n" ); document.write( "axes draw the line y=5(x-2) use a scale of 1 cm to 1 unit on the x axis and 1cm
\n" ); document.write( "to 5 unit on the y axis.From your graph find the roots of equations 3x(4-x)
\n" ); document.write( "write down the maximum value of y=3x(4-x) and deduce the root of the equation.
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document.write( "Make tables of values for the two graphs from -2 to 6.\r\n" );
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document.write( "y=3x(4-x)          y=5(x-2)\r\n" );
document.write( "x | y              x| y\r\n" );
document.write( "-2|-36            -2|-20 \r\n" );
document.write( "-1|-15            -1|-15\r\n" );
document.write( " 0|  0             0|-10\r\n" );
document.write( " 1|  9             1| -5 \r\n" );
document.write( " 2| 12             2|  0\r\n" );
document.write( " 3|  9             3|  5\r\n" );
document.write( " 4|  0             4| 10\r\n" );
document.write( " 5|-15             5| 15\r\n" );
document.write( " 6|-36             6| 20\r\n" );
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document.write( "Plot the points.  The graph below does not contain all the points, but it is\r\n" );
document.write( "to scale. Each block is 1  cm on the x-axis to 5 cm on the y-axis, but you will\r\n" );
document.write( "need to extend the graph to be able to show the first and last points on the\r\n" );
document.write( "tables of values. \r\n" );
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document.write( "From the graph we can deduce the maximum value of the equation y=3x(4-x),\r\n" );
document.write( "the red graph, is 12 for the point (2,12) is the highest point, and we can\r\n" );
document.write( "deduce that the roots of the equation y=3x(4-x) are 0 and 4 for those are\r\n" );
document.write( "the values on the x-axis where the red graph crosses the x-axis.\r\n" );
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document.write( "We can also show that the roots of y=3x(4-x) are 0 and 4 using algebra\r\n" );
document.write( "instead of deducing them from the graph. We do that by setting y=0 and\r\n" );
document.write( "solving for x:\r\n" );
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document.write( "y = 3x(4-x)\r\n" );
document.write( "0 = 3x(4-x)\r\n" );
document.write( "Divide both sides by 3\r\n" );
document.write( "0/3 = x(4-x)2\r\n" );
document.write( "0 = 4x-x2\r\n" );
document.write( "4x-x2 = 0\r\n" );
document.write( "Factor out x\r\n" );
document.write( "x(4-x) = 0\r\n" );
document.write( "x=0; 4-x=0\r\n" );
document.write( "      -x=-4\r\n" );
document.write( "       x=4\r\n" );
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document.write( "Edwin
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