document.write( "Question 145839: I have the following quadratic equation that I have been trying to graph for like an hour and I am having the toughest time with it. Could someone please help me ASAP???\r
\n" ); document.write( "\n" ); document.write( "Thanks!\r
\n" ); document.write( "\n" ); document.write( "Maggie\r
\n" ); document.write( "\n" ); document.write( "3x2(squared)-x-1 = 0\r
\n" ); document.write( "\n" ); document.write( "Could you provide each step so that I may see where I have messed up. I know that I need to have ax2 + bx - c =0, so a=3, b=-1 and c=-1.\r
\n" ); document.write( "\n" ); document.write( "I've have plugged these into the -b +/- b2-4ac over 2a???? But for some reason, I get screwed up about mid way through.\r
\n" ); document.write( "\n" ); document.write( "Help!!! \n" ); document.write( "

Algebra.Com's Answer #106432 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
You don't need to use the quadratic formula to graph this. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=3x%5E2-1x-1\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So let's find the first point:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2-1x-1\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=3%28-2%29%5E2-1%28-2%29-1\"$ Plug in $\"x=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=13\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our 1st point is (-2,13)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2-1x-1\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=3%28-1%29%5E2-1%28-1%29-1\"$ Plug in $\"x=-1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=3\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-1,3)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2-1x-1\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%280%29=3%280%29%5E2-1%280%29-1\"$ Plug in $\"x=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=-1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our 3rd point is (0,-1)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2-1x-1\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%281%29=3%281%29%5E2-1%281%29-1\"$ Plug in $\"x=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our 4th point is (1,1)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x%5E2-1x-1\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%282%29=3%282%29%5E2-1%282%29-1\"$ Plug in $\"x=2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our 5th point is (2,9)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " x y
 -2 13
 -1 3
 0 -1
 1 1
 2 9\r\n" );
document.write( "

Now plot the points\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=3x%5E2-1x-1\"$ (note: the more points you plot, the easier it is to draw the graph)\r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( "

\n" );