document.write( "Question 125371: I am having a difficult time with this equation and graphing it. y=x^2-4x \n" ); document.write( "

Algebra.Com's Answer #91893 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E2-4x\"$ , we need to plot some points.\r
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\n" ); document.write( "\n" ); document.write( "We can start at any x value, so lets start at x=-1\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%28-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%28-1%29%5E2-4%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%281%29-4%28-1%29\"$ Evaluate $\"%28-1%29%5E2\"$ to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=1%2B4\"$ Multiply -4 and -1 to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=5\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , $\"f%28x%29=5\"$ \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 $\"f%280%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%5E2-4%280%29\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29-4%280%29\"$ Evaluate $\"1%280%29%5E2\"$ to get 10\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=00\"$ Multiply -4 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"f%28x%29=0\"$ \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( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E2-4%281%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-4%281%29\"$ Evaluate $\"1%281%29%5E2\"$ to get 11\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=1-4\"$ Multiply -4 and 1 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"f%28x%29=-3\"$ \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 $\"f%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%282%29%5E2-4%282%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%284%29-4%282%29\"$ Evaluate $\"1%282%29%5E2\"$ to get 14\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=4-8\"$ Multiply -4 and 2 to get -8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"f%28x%29=-4\"$ \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 $\"f%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%283%29%5E2-4%283%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%289%29-4%283%29\"$ Evaluate $\"1%283%29%5E2\"$ to get 19\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=9-12\"$ Multiply -4 and 3 to get -12\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"f%28x%29=-3\"$ \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 $\"f%284%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%284%29%5E2-4%284%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%2816%29-4%284%29\"$ Evaluate $\"1%284%29%5E2\"$ to get 116\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=16-16\"$ Multiply -4 and 4 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=0\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"f%28x%29=0\"$ \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 $\"f%285%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-4x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=%285%29%5E2-4%285%29\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=%2825%29-4%285%29\"$ Evaluate $\"1%285%29%5E2\"$ to get 125\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=25-20\"$ Multiply -4 and 5 to get -20\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=5\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"f%28x%29=5\"$ \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 5
 0 0
 1 -3
 2 -4
 3 -3
 4 0
 5 5\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 $\"y=x%5E2-4x\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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