document.write( "Question 187667This question is from textbook Mathematical Excursions
\n" ); document.write( ": I am having trouble finding book help and with my notes to learn/solve this problem. \r
\n" ); document.write( "\n" ); document.write( "Graph each equation:\r
\n" ); document.write( "\n" ); document.write( "Y=1/2xsquared\r
\n" ); document.write( "\n" ); document.write( "Can you help me? \n" ); document.write( "

Algebra.Com's Answer #140695 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "In order to graph $\"y=%281%2F2%29x%5E2\"$ , we need to plot a few points\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%28-4%29%5E2\"$ Plug in $\"x=-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%2816%29\"$ Square -4 to get 16.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%2816%29%2F2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8\"$ Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-4\"$ , then $\"y=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (-4,8)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%28-3%29%5E2\"$ Plug in $\"x=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%289%29\"$ Square -3 to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%289%29%2F2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4.5\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-3\"$ , then $\"y=4.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (-3,4.5)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%28-2%29%5E2\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%284%29\"$ Square -2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%2F2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-2\"$ , then $\"y=2\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (-2,2)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%28-1%29%5E2\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%281%29\"$ Square -1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%2F2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.5\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-1\"$ , then $\"y=0.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (-1,0.5)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%280%29%5E2\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%280%29\"$ Square 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280%29%2F2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=0\"$ , then $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (0,0)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%281%29%5E2\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%281%29\"$ Square 1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%2F2\"$ Multiply.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0.5\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=0.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (1,0.5)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%282%29%5E2\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%284%29\"$ Square 2 to get 4.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%2F2\"$ Multiply.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ Reduce.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=2\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (2,2)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%283%29%5E2\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%289%29\"$ Square 3 to get 9.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%289%29%2F2\"$ Multiply.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4.5\"$ Divide.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=3\"$ , then $\"y=4.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (3,4.5)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29x%5E2\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%284%29%5E2\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F2%29%2816%29\"$ Square 4 to get 16.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%2816%29%2F2\"$ Multiply.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=8\"$ Reduce.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "This means that we have the point (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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x	y
-4	8
-3	4.5
-2	2
-1	0.5
0	0
1	0.5
2	2
3	4.5
4	8

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\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=%281%2F2%29x%5E2\"$ :\r
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Graph of $\"y=%281%2F2%29x%5E2\"$ \n" ); document.write( "

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