document.write( "Question 78255: hi i am having trouble working out how to do these graphs.
\n" ); document.write( "could someone show me how to work it out and if they could do the graphs that would be much appreciated x\r
\n" ); document.write( "\n" ); document.write( "Question:
\n" ); document.write( "plot a graph of the following curves and write down their co-ordinates of their intersection with the x- axis:
\n" ); document.write( "a, y=x²-x-2
\n" ); document.write( "b, y=2x²-3x-9\r
\n" ); document.write( "\n" ); document.write( "plot the graphs between x=-2 and x=+3\r
\n" ); document.write( "\n" ); document.write( "thanks for your help x \n" ); document.write( "

Algebra.Com's Answer #56122 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"y=x%5E2-x-2\"$ lets make a table:
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\r\n" );
document.write( "\r\n" );
document.write( "      x      y\r\n" );
document.write( "   -5.0   28.0\r\n" );
document.write( "   -4.0   18.0\r\n" );
document.write( "   -3.0   10.0\r\n" );
document.write( "   -2.0    4.0\r\n" );
document.write( "   -1.0    0.0\r\n" );
document.write( "    0.0   -2.0\r\n" );
document.write( "    1.0   -2.0\r\n" );
document.write( "    2.0    0.0\r\n" );
document.write( "    3.0    4.0\r\n" );
document.write( "    4.0   10.0\r\n" );
document.write( "    5.0   18.0\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Now draw a parabola through these points\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%5E2-x-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=2x%5E2-3x-9\"$ lets make a table:
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "     x      y\r\n" );
document.write( "   -5.0   56.0\r\n" );
document.write( "   -4.0   35.0\r\n" );
document.write( "   -3.0   18.0\r\n" );
document.write( "   -2.0    5.0\r\n" );
document.write( "   -1.0   -4.0\r\n" );
document.write( "    0.0   -9.0\r\n" );
document.write( "    1.0  -10.0\r\n" );
document.write( "    2.0   -7.0\r\n" );
document.write( "    3.0    0.0\r\n" );
document.write( "    4.0   11.0\r\n" );
document.write( "    5.0   26.0\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Now draw a parabola through these points\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%5E2-3x-9%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "So now use the quadratic formula for each case to find the x-intercepts\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B-1x%2B-2+=+0\"$ ) has the following solutons:
\n" ); document.write( "
\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-1%29%5E2-4%2A1%2A-2=9\"$ .
\n" ); document.write( "
\n" ); document.write( " Discriminant d=9 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--1%2B-sqrt%28+9+%29%29%2F2%5Ca\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+2\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+9+%29%29%2F2%5C1+=+-1\"$
\n" ); document.write( "
\n" ); document.write( " Quadratic expression $\"1x%5E2%2B-1x%2B-2\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B-1x%2B-2+=+1%28x-2%29%2A%28x--1%29\"$
\n" ); document.write( " Again, the answer is: 2, -1.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-2+%29\"$

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the x-intercepts are (-1,0) and (2,0)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"2x%5E2%2B-3x%2B-9+=+0\"$ ) has the following solutons:
\n" ); document.write( "
\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-9=81\"$ .
\n" ); document.write( "
\n" ); document.write( " Discriminant d=81 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--3%2B-sqrt%28+81+%29%29%2F2%5Ca\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+3\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-3%29-sqrt%28+81+%29%29%2F2%5C2+=+-1.5\"$
\n" ); document.write( "
\n" ); document.write( " Quadratic expression $\"2x%5E2%2B-3x%2B-9\"$ can be factored:
\n" ); document.write( " $\"2x%5E2%2B-3x%2B-9+=+2%28x-3%29%2A%28x--1.5%29\"$
\n" ); document.write( " Again, the answer is: 3, -1.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-9+%29\"$

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\n" ); document.write( "\n" ); document.write( "So the x-intercepts are (-1.5,0) and (3,0) \n" ); document.write( "

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