document.write( "Question 88249: Graph the following equation: y = –x^2 + 2x \n" ); document.write( "

Algebra.Com's Answer #64083 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=-x%5E2%2B2x\"$ , we need to plot some points.
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%28-2%29%5E2%2B2%28-2%29\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B2%28-2%29\"$ Raise -2 to the second power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B-4\"$ Multiply 2 by -2 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-8\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-2,-8)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%28-1%29%5E2%2B2%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B2%28-1%29\"$ Raise -1 to the second power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B-2\"$ Multiply 2 by -1 to get -2\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-1,-3)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%280%29%5E2%2B2%280%29\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%280%29%2B2%280%29\"$ Raise 0 to the second power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%280%29%2B0\"$ Multiply 2 by 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (0,0)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%5E2%2B2%281%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B2%281%29\"$ Raise 1 to the second power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B2\"$ Multiply 2 by 1 to get 2\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (1,1)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%282%29%5E2%2B2%282%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B2%282%29\"$ Raise 2 to the second power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B4\"$ Multiply 2 by 2 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (2,0)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%283%29%5E2%2B2%283%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%289%29%2B2%283%29\"$ Raise 3 to the second power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%289%29%2B6\"$ Multiply 2 by 3 to get 6\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (3,-3)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%5E2%2B2%284%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%2816%29%2B2%284%29\"$ Raise 4 to the second power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%2816%29%2B8\"$ Multiply 2 by 4 to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-8\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (4,-8)\r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
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document.write( " x y
 -2 -8
 -1 -3
 0 0
 1 1
 2 0
 3 -3
 4 -8\r\n" );
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Now plot the points\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-x%5E2%2B2x\"$ \r
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