document.write( "Question 88246: Graph the following equation: y = –x^2 + 1 \n" ); document.write( "

Algebra.Com's Answer #64084 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 $\"y=-x%5E2%2B1\"$ , we need to plot some points.
\n" ); document.write( "We can start at any x value, so lets start at x=-3\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%28-3%29%5E2%2B1\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%289%29%2B1\"$ Raise -3 to the second power to get 9\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 (-3,-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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%28-2%29%5E2%2B1\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B1\"$ Raise -2 to the second power to get 4\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 (-2,-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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%28-1%29%5E2%2B1\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B1\"$ Raise -1 to the second power to get 1\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 (-1,0)\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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%280%29%5E2%2B1\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%280%29%2B1\"$ Raise 0 to the second power to get 0\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 (0,1)\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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%5E2%2B1\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%281%29%2B1\"$ Raise 1 to the second power to get 1\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 (1,0)\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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%282%29%5E2%2B1\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%284%29%2B1\"$ Raise 2 to the second power to get 4\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 (2,-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( " $\"y=-x%5E2%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%283%29%5E2%2B1\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=-%289%29%2B1\"$ Raise 3 to the second power to get 9\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 (3,-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
 -3 -8
 -2 -3
 -1 0
 0 1
 1 0
 2 -3
 3 -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 $\"y=-x%5E2%2B1\"$ \r
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