document.write( "Question 102742: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). Could someone help me please?
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Algebra.Com's Answer #74746 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the axis of symmetry, use this formula:\r
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\n" ); document.write( "\n" ); document.write( " $\"x=-b%2F%282a%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "From the equation $\"y=x%5E2-5x%2B4\"$ we can see that a=1 and b=-5\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%28--5%29%2F%282%2A1%29\"$ Plug in b=-5 and a=1\r
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\n" ); document.write( "\n" ); document.write( " $\"x=5%2F%282%2A1%29\"$ Negate -5 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%285%29%2F2\"$ Multiply 2 and 1 to get 2\r
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\n" ); document.write( "\n" ); document.write( "So the axis of symmetry is $\"x=5%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the x-coordinate of the vertex is $\"x=5%2F2\"$ (which is $\"x=2.5\"$ in decimal form). Lets plug this into the equation to find the y-coordinate of the vertex.\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%282.5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282.5%29=%282.5%29%5E2-5%282.5%29%2B4\"$ Plug in $\"x=2.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282.5%29=%286.25%29-5%282.5%29%2B4\"$ Raise 2.5 to the second power to get 6.25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282.5%29=%286.25%29-12.5%2B4\"$ Multiply 5 by 2.5 to get 12.5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282.5%29=-2.25\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So the vertex is (2.5,-2.25)\r
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\n" ); document.write( "\n" ); document.write( "Since the x-coordinate is 2.5, this means the axis of symmetry is $\"x=2.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now lets find 2 other points to the left of the vertex\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%280%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%5E2-5%280%29%2B4\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29-5%280%29%2B4\"$ Raise 0 to the second power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29-0%2B4\"$ Multiply 5 by 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=4\"$ Remove any zero terms\r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (0,4)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E2-5%281%29%2B4\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-5%281%29%2B4\"$ Raise 1 to the second power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-5%2B4\"$ Multiply 5 by 1 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=0\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (1,0)\r
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\n" ); document.write( "\n" ); document.write( "Now remember, the parabola is symmetrical about the axis of symmetry (which is $\"x=2.5\"$ )\r
\n" ); document.write( "\n" ); document.write( "This means the y-value for $\"x=1\"$ is equal to the y-value of $\"x=4\"$ . So when $\"x=4\"$ , $\"y=0\"$ .\r
\n" ); document.write( "\n" ); document.write( "Also, the y-value for $\"x=0\"$ is equal to the y-value of $\"x=5\"$ . So when $\"x=5\"$ , $\"y=4\"$ .\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
 0 4
 1 0
 2.5 -2.25
 4 0
 5 4\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice if you graph the equation $\"y=x%5E2-5x%2B4\"$ with the axis of symmetry you get\r
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Graph of $\"y=x%5E2-5x%2B4\"$ through the given points. Notice the axis of symmetry is the equation $\"x=2.5\"$ which is the vertical line through the vertex of the parabola. \n" ); document.write( "

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