document.write( "Question 150929: sketch the graph of f(x) + (x-3)2 + 1 \n" ); document.write( "

Algebra.Com's Answer #110870 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=%28x-3%29%5E2+%2B+1\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ note: you can start at any x value. \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280-3%29%5E2+%2B+1\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=10\"$ . So we have the point (0,10).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281-3%29%5E2+%2B+1\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=5\"$ . So we have the point (1,5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282-3%29%5E2+%2B+1\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=2\"$ . So we have the point (2,2).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%283-3%29%5E2+%2B+1\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"y=1\"$ . So we have the point (3,1).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%284-3%29%5E2+%2B+1\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"y=2\"$ . So we have the point (4,2).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%285-3%29%5E2+%2B+1\"$ Plug in $\"x=5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"y=5\"$ . So we have the point (5,5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28x-3%29%5E2+%2B+1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%286-3%29%5E2+%2B+1\"$ Plug in $\"x=6\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=10\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=6\"$ , $\"y=10\"$ . So we have the point (6,10).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
0 10
1 5
2 2
3 1
4 2
5 5
6 10\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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Graph:

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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=%28x-3%29%5E2+%2B+1\"$ :\r
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Graph of $\"y=%28x-3%29%5E2+%2B+1\"$ \n" ); document.write( "

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