document.write( "Question 128612: Make a table of at least 7 ordered pairs that satisfy the equation $\"y=x%5E2-3\"$ . Then use your table to graph the function. \n" ); document.write( "

Algebra.Com's Answer #94091 by jim_thompson5910(35256) $\"\"$ $\"About$

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In order to generate ordered pairs, we need to plot evaluate some x values to get some y values to get the points.\r
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\n" ); document.write( "\n" ); document.write( "So let's find the first point:\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=1%28-5%29%5E2-3\"$ Plug in $\"x=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=1%2A25-3\"$ Raise -5 to the 2nd power to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=25-3\"$ Multiply 1 and 25 to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=22\"$ Subtract 3 from 25 to get 22\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-5\"$ , we have $\"y=22\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-5,22)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=1%28-4%29%5E2-3\"$ Plug in $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=1%2A16-3\"$ Raise -4 to the 2nd power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=16-3\"$ Multiply 1 and 16 to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=13\"$ Subtract 3 from 16 to get 13\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-4\"$ , we have $\"y=13\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-4,13)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=1%28-3%29%5E2-3\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=1%2A9-3\"$ Raise -3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=9-3\"$ Multiply 1 and 9 to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=6\"$ Subtract 3 from 9 to get 6\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , we have $\"y=6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-3,6)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1%28-2%29%5E2-3\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1%2A4-3\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=4-3\"$ Multiply 1 and 4 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1\"$ Subtract 3 from 4 to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (-2,1)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%28-1%29%5E2-3\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%2A1-3\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1-3\"$ Multiply 1 and 1 to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2\"$ Subtract 3 from 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (-1,-2)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%280%29%5E2-3\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%2A0-3\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-3\"$ Multiply 1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-3\"$ Subtract 3 from 0 to get -3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (0,-3)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1%281%29%5E2-3\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1%2A1-3\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1-3\"$ Multiply 1 and 1 to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2\"$ Subtract 3 from 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (1,-2)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=1%282%29%5E2-3\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=1%2A4-3\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=4-3\"$ Multiply 1 and 4 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=1\"$ Subtract 3 from 4 to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 8th point is (2,1)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=1%283%29%5E2-3\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=1%2A9-3\"$ Raise 3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=9-3\"$ Multiply 1 and 9 to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=6\"$ Subtract 3 from 9 to get 6\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 9th point is (3,6)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=1%284%29%5E2-3\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=1%2A16-3\"$ Raise 4 to the 2nd power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=16-3\"$ Multiply 1 and 16 to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=13\"$ Subtract 3 from 16 to get 13\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , we have $\"y=13\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 10th point is (4,13)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2-3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=1%285%29%5E2-3\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=1%2A25-3\"$ Raise 5 to the 2nd power to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=25-3\"$ Multiply 1 and 25 to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=22\"$ Subtract 3 from 25 to get 22\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , we have $\"y=22\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 11th point is (5,22)\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
 -5 22
 -4 13
 -3 6
 -2 1
 -1 -2
 0 -3
 1 -2
 2 1
 3 6
 4 13
 5 22\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now plot the points. Note: you need to use Firefox to see the next two graphs.\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=1x%5E2-3\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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