document.write( "Question 114165: Use a table of solutions to graph the quadratic equation y = x^2 + 1 \n" ); document.write( "

Algebra.Com's Answer #83117 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's find values of y when x is from -3 to 3\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( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%28-3%29%5E2%2B1\"$ Plug in $\"x=-3\"$ . In other words, replace each x with -3.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%289%29%2B1\"$ Evaluate $\"%28-3%29%5E2\"$ to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=10\"$ 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( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%28-2%29%5E2%2B1\"$ Plug in $\"x=-2\"$ . In other words, replace each x with -2.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%284%29%2B1\"$ Evaluate $\"%28-2%29%5E2\"$ to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=5\"$ 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( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%28-1%29%5E2%2B1\"$ Plug in $\"x=-1\"$ . In other words, replace each x with -1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%281%29%2B1\"$ Evaluate $\"%28-1%29%5E2\"$ to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=2\"$ 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( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%5E2%2B1\"$ Plug in $\"x=0\"$ . In other words, replace each x with 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%2B1\"$ Evaluate $\"%280%29%5E2\"$ to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1\"$ 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 $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E2%2B1\"$ Plug in $\"x=1\"$ . In other words, replace each x with 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%2B1\"$ Evaluate $\"%281%29%5E2\"$ to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=2\"$ 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 $\"f%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%282%29%5E2%2B1\"$ Plug in $\"x=2\"$ . In other words, replace each x with 2.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%284%29%2B1\"$ Evaluate $\"%282%29%5E2\"$ to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=5\"$ 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 $\"f%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B1\"$ Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%283%29%5E2%2B1\"$ Plug in $\"x=3\"$ . In other words, replace each x with 3.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%289%29%2B1\"$ Evaluate $\"%283%29%5E2\"$ to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=10\"$ 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
 -3 10
 -2 5
 -1 2
 0 1
 1 2
 2 5
 3 10\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 $\"y=x%5E2%2B1\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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