document.write( "Question 116779: Show me how to graph y=x^2+5x+3 \n" ); document.write( "

Algebra.Com's Answer #84898 by jim_thompson5910(35256) $\"\"$ $\"About$

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To graph $\"y=x%5E2%2B5x%2B3\"$ simply plot a sequence of points and connect them. In other words, find y values for some given x values and plot the points (x,y).\r
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\n" ); document.write( "\n" ); document.write( "So let's start at x=-6\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-6%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-6%29=%28-6%29%5E2%2B5%28-6%29%2B3\"$ Plug in $\"x=-6\"$ . In other words, replace each x with -6.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-6%29=%2836%29%2B5%28-6%29%2B3\"$ Evaluate $\"%28-6%29%5E2\"$ to get 36.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-6%29=%2836%29%2B-30%2B3\"$ Multiply 5 and -6 to get -30\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-6%29=9\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%28-5%29%5E2%2B5%28-5%29%2B3\"$ Plug in $\"x=-5\"$ . In other words, replace each x with -5.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%2825%29%2B5%28-5%29%2B3\"$ Evaluate $\"%28-5%29%5E2\"$ to get 25.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%2825%29%2B-25%2B3\"$ Multiply 5 and -5 to get -25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%28-4%29%5E2%2B5%28-4%29%2B3\"$ Plug in $\"x=-4\"$ . In other words, replace each x with -4.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%2816%29%2B5%28-4%29%2B3\"$ Evaluate $\"%28-4%29%5E2\"$ to get 16.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%2816%29%2B-20%2B3\"$ Multiply 5 and -4 to get -20\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=-1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%28-3%29%5E2%2B5%28-3%29%2B3\"$ Plug in $\"x=-3\"$ . In other words, replace each x with -3.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%289%29%2B5%28-3%29%2B3\"$ Evaluate $\"%28-3%29%5E2\"$ to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%289%29%2B-15%2B3\"$ Multiply 5 and -3 to get -15\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%28-2%29%5E2%2B5%28-2%29%2B3\"$ Plug in $\"x=-2\"$ . In other words, replace each x with -2.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%284%29%2B5%28-2%29%2B3\"$ Evaluate $\"%28-2%29%5E2\"$ to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%284%29%2B-10%2B3\"$ Multiply 5 and -2 to get -10\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%28-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%28-1%29%5E2%2B5%28-1%29%2B3\"$ Plug in $\"x=-1\"$ . In other words, replace each x with -1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%281%29%2B5%28-1%29%2B3\"$ Evaluate $\"%28-1%29%5E2\"$ to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%281%29%2B-5%2B3\"$ Multiply 5 and -1 to get -5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%280%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%5E2%2B5%280%29%2B3\"$ Plug in $\"x=0\"$ . In other words, replace each x with 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%2B5%280%29%2B3\"$ Evaluate $\"%280%29%5E2\"$ to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%2B0%2B3\"$ Multiply 5 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "-----------Now let's evaluate another value---------\r
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\n" ); document.write( "\n" ); document.write( "Let's evaluate $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B5x%2B3\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E2%2B5%281%29%2B3\"$ Plug in $\"x=1\"$ . In other words, replace each x with 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%2B5%281%29%2B3\"$ Evaluate $\"%281%29%5E2\"$ to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%2B5%2B3\"$ Multiply 5 and 1 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=9\"$ Now combine like terms\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
 -6 9
 -5 3
 -4 -1
 -3 -3
 -2 -3
 -1 -1
 0 3
 1 9\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 $\"y=x%5E2%2B5x%2B3\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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