document.write( "Question 131616: y=x^2+2 \n" ); document.write( "

Algebra.Com's Answer #96079 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to graph?\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=1x%5E2%2B2\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\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( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=1%28-3%29%5E2%2B2\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=1%2A9%2B2\"$ Raise -3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=9%2B2\"$ Multiply 1 and 9 to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=11\"$ Add 9 and 2 to get 11\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , we have $\"y=11\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-3,11)\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( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1%28-2%29%5E2%2B2\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1%2A4%2B2\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=4%2B2\"$ Multiply 1 and 4 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=6\"$ Add 4 and 2 to get 6\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-2,6)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%28-1%29%5E2%2B2\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%2A1%2B2\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%2B2\"$ Multiply 1 and 1 to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=3\"$ Add 1 and 2 to get 3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-1,3)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%280%29%5E2%2B2\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%2A0%2B2\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B2\"$ Multiply 1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=2\"$ Add 0 and 2 to get 2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (0,2)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1%281%29%5E2%2B2\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1%2A1%2B2\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1%2B2\"$ Multiply 1 and 1 to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=3\"$ Add 1 and 2 to get 3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (1,3)\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( " $\"f%28x%29=1x%5E2%2B2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=1%282%29%5E2%2B2\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=1%2A4%2B2\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=4%2B2\"$ Multiply 1 and 4 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=6\"$ Add 4 and 2 to get 6\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=6\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (2,6)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=1%283%29%5E2%2B2\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=1%2A9%2B2\"$ Raise 3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=9%2B2\"$ Multiply 1 and 9 to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=11\"$ Add 9 and 2 to get 11\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=11\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (3,11)\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 11
 -2 6
 -1 3
 0 2
 1 3
 2 6
 3 11\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 $\"y=1x%5E2%2B2\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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