document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150372>Question 150372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Graph the following quadratic functions<BR>\n" );
document.write( "F(x)= -x^2-2x+2<BR>\n" );
document.write( "F(x)= -x^2+3x+2<BR>\n" );
document.write( "F(x)= x^2+2x+2<BR>\n" );
document.write( "F(x)= x^2-2x-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. Solve the equation and check the proposed solutions   2/x+2/x+1 = 3x-1/x^2-1. Show all work<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110464 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Graph the following quadratic functions<BR>\n" );
document.write( "a. F(x)= -x^2-2x+2<BR>\n" );
document.write( "b. F(x)= -x^2+3x+2<BR>\n" );
document.write( "c. F(x)= x^2+2x+2<BR>\n" );
document.write( "d. F(x)= x^2-2x-2 \r<BR>\n" );
document.write( "\n" );
document.write( "2. Solve the equation and check the proposed solutions 2/x+2/x+1 = 3x-1/x^2-1. Show all work<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "1a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+=+-x%5E2-2x%2B2 ALIGN=MIDDLE  ALT=\"F%28x%29+=+-x%5E2-2x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B2+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-2%29%5E2-4%2A-1%2A2=12 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A-1%2A2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=12 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C-1+=+-2.73205080756888 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C-1+=+-2.73205080756888\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C-1+=+0.732050807568877 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C-1+=+0.732050807568877\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B2 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B2+=+%28x--2.73205080756888%29%2A%28x-0.732050807568877%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B2+=+%28x--2.73205080756888%29%2A%28x-0.732050807568877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.73205080756888, 0.732050807568877.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Further simplified:<BR>\n" );
document.write( "x1 = -1+sqrt(3)<BR>\n" );
document.write( "x2 = -1-sqrt(3)<BR>\n" );
document.write( "++++++++++++++++++<BR>\n" );
document.write( "The other 3 are done the same way.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "2. This is ambiguous and needs clarification.<BR>\n" );
document.write( "The right side could mean 3x - (1/x^2) - 1, or 3x - 1/(x^2-1). Add parentheses, they're free. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );