document.write( "Question 83862: Graph and answer the questions.
\n" ); document.write( "f(x) = -x^2 + 4x - 1\r
\n" ); document.write( "\n" ); document.write( "What are the coordinates of the vertex?
\n" ); document.write( "What is the domain?
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Algebra.Com's Answer #60318 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"-x%5E2%2B4x-1\"$ , we need to plot some points.
\n" ); document.write( " So we can start at any x value. So lets start at x=-1
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%28-1%29%5E2%2B4%28-1%29-1\"$ Plug in $\"x=-1\"$
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\n" ); document.write( " $\"-%28-1%29%5E2%2B4%28-1%29-1=-6\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ $\"y=-6\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 1st point is (-1,-6)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%280%29%5E2%2B4%280%29-1\"$ Plug in $\"x=0\"$
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\n" ); document.write( " $\"-%280%29%5E2%2B4%280%29-1=-1\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ $\"y=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 2nd point is (0,-1)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%281%29%5E2%2B4%281%29-1\"$ Plug in $\"x=1\"$
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\n" ); document.write( " $\"-%281%29%5E2%2B4%281%29-1=2\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ $\"y=2\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 3rd point is (1,2)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%282%29%5E2%2B4%282%29-1\"$ Plug in $\"x=2\"$
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\n" ); document.write( " $\"-%282%29%5E2%2B4%282%29-1=3\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ $\"y=3\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 4th point is (2,3)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%283%29%5E2%2B4%283%29-1\"$ Plug in $\"x=3\"$
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\n" ); document.write( " $\"-%283%29%5E2%2B4%283%29-1=2\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ $\"y=2\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 5th point is (3,2)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%284%29%5E2%2B4%284%29-1\"$ Plug in $\"x=4\"$
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\n" ); document.write( " $\"-%284%29%5E2%2B4%284%29-1=-1\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ $\"y=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 6th point is (4,-1)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B4x-1\"$ Start with the given equation
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\n" ); document.write( " $\"y=-%285%29%5E2%2B4%285%29-1\"$ Plug in $\"x=5\"$
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\n" ); document.write( " $\"-%285%29%5E2%2B4%285%29-1=-6\"$ Calculate the y value\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ $\"y=-6\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 7th point is (5,-6)\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
 -1 -6
 0 -1
 1 2
 2 3
 3 2
 4 -1
 5 -6\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, this is the graph of $\"-x%5E2%2B4x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So from the graph we can see that the vertex is (2,3), the domain is the element of all real numbers (any number will work for x) and the range is $\"y%3C=3\"$ \n" ); document.write( "

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