document.write( "Question 130124: f(x) = -2x^2 - 8x + 3 \n" ); document.write( "

Algebra.Com's Answer #95058 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to graph?\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=-2x%5E2-8x%2B3\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\r
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\n" ); document.write( "\n" ); document.write( "So let's find the first point:\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E2-8x%2B3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-2%28-5%29%5E2-8%28-5%29%2B3\"$ Plug in $\"x=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-2%2A25-8%2A-5%2B3\"$ Raise -5 to the 2nd power to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-50-8%2A-5%2B3\"$ Multiply -2 and 25 to get -50\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-50--40%2B3\"$ Multiply 8 and -5 to get -40\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-10%2B3\"$ Subtract -40 from -50 to get -10\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=-7\"$ Add -10 and 3 to get -7\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-5\"$ , we have $\"y=-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-5,-7)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E2-8x%2B3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=-2%28-4%29%5E2-8%28-4%29%2B3\"$ Plug in $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=-2%2A16-8%2A-4%2B3\"$ Raise -4 to the 2nd power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=-32-8%2A-4%2B3\"$ Multiply -2 and 16 to get -32\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=-32--32%2B3\"$ Multiply 8 and -4 to get -32\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=0%2B3\"$ Subtract -32 from -32 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=3\"$ Add 0 and 3 to get 3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-4\"$ , we have $\"y=3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-4,3)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E2-8x%2B3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-2%28-3%29%5E2-8%28-3%29%2B3\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-2%2A9-8%2A-3%2B3\"$ Raise -3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-18-8%2A-3%2B3\"$ Multiply -2 and 9 to get -18\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-18--24%2B3\"$ Multiply 8 and -3 to get -24\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=6%2B3\"$ Subtract -24 from -18 to get 6\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=9\"$ Add 6 and 3 to get 9\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , we have $\"y=9\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-3,9)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E2-8x%2B3\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-2%28-2%29%5E2-8%28-2%29%2B3\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-2%2A4-8%2A-2%2B3\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-8-8%2A-2%2B3\"$ Multiply -2 and 4 to get -8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-8--16%2B3\"$ Multiply 8 and -2 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=8%2B3\"$ Subtract -16 from -8 to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=11\"$ Add 8 and 3 to get 11\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=11\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (-2,11)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2%28-1%29%5E2-8%28-1%29%2B3\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2%2A1-8%2A-1%2B3\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2-8%2A-1%2B3\"$ Multiply -2 and 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2--8%2B3\"$ Multiply 8 and -1 to get -8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=6%2B3\"$ Subtract -8 from -2 to get 6\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=9\"$ Add 6 and 3 to get 9\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=9\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (-1,9)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-2%280%29%5E2-8%280%29%2B3\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-2%2A0-8%2A0%2B3\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-8%2A0%2B3\"$ Multiply -2 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-0%2B3\"$ Multiply 8 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B3\"$ Subtract 0 from 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=3\"$ Add 0 and 3 to get 3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (0,3)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2%281%29%5E2-8%281%29%2B3\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2%2A1-8%2A1%2B3\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2-8%2A1%2B3\"$ Multiply -2 and 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2-8%2B3\"$ Multiply 8 and 1 to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-10%2B3\"$ Subtract 8 from -2 to get -10\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-7\"$ Add -10 and 3 to get -7\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (1,-7)\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
 -5 -7
 -4 3
 -3 9
 -2 11
 -1 9
 0 3
 1 -7\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 $\"y=-2x%5E2-8x%2B3\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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