document.write( "Question 133355This question is from textbook
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\n" ); document.write( "y=-6x^2 \n" ); document.write( "

Algebra.Com's Answer #97541 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to graph these? I'll do the first two to get you started.\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=-1x%5E2\"$ , 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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-1%28-3%29%5E2\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-1%2A9\"$ Raise -3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-9\"$ Multiply -1 and 9 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 1st point is (-3,-9)\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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%28-2%29%5E2\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%2A4\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-4\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-2,-4)\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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%28-1%29%5E2\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2A1\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-1,-1)\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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%280%29%5E2\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%2A0\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0\"$ Multiply -1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (0,0)\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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%281%29%5E2\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2A1\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (1,-1)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%282%29%5E2\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%2A4\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (2,-4)\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( " $\"f%28x%29=-1x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%283%29%5E2\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%2A9\"$ Raise 3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9\"$ Multiply -1 and 9 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 7th point is (3,-9)\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 -9
 -2 -4
 -1 -1
 0 0
 1 -1
 2 -4
 3 -9\r\n" );
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Now plot the points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-1x%5E2\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=-4x%5E2\"$ , 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( " $\"f%28x%29=-4x%5E2\"$ Start with the given function\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-4%28-1%29%5E2\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-4%2A1\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-4\"$ Multiply -4 and 1 to get -4\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-1,-4)\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( " $\"f%28x%29=-4x%5E2\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-4%280%29%5E2\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-4%2A0\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0\"$ Multiply -4 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (0,0)\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( " $\"f%281%29=-4%281%29%5E2\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-4%2A1\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-4\"$ Multiply -4 and 1 to get -4\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (1,-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
 -1 -4
 0 0
 1 -4\r\n" );
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Now plot the points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-4x%5E2\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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