document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23392>Question 23392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you in advance for you help with this equation.  I really appreciate it.<BR>\n" );
document.write( "Question 1<BR>\n" );
document.write( "The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2 + 300x - 200.  What is the total profit if 500 are sold?  For what value of x will the profit be at a maximum?\r<BR>\n" );
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document.write( "Question 2\r<BR>\n" );
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document.write( "Solve the equation by using the quadratic equation.\r<BR>\n" );
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document.write( "y^2 + 6y + 4 = 0\r<BR>\n" );
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document.write( "Question 3\r<BR>\n" );
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document.write( "Solve the equation<BR>\n" );
document.write( "b+17/b^2-1 - 1/b+1 = b-2/b-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12189 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1: In place of \"x\" put 500. Then evaluate.<BR>\n" );
document.write( "You have a quadratic with a=-0.2, b=300, c=-200<BR>\n" );
document.write( "The max is at x=-b/2a = 300/0.4 = 7500<BR>\n" );
document.write( "In place of \"x\" in the original equation put 7500 to <BR>\n" );
document.write( "find the corresponding P(7500)<BR>\n" );
document.write( "#2:a=1,b=6,c=4<BR>\n" );
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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=quadratic.solver>SOLVE quadratic equation with variable</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%2B6x%2B4+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B4+=+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=%286%29%5E2-4%2A1%2A4=20 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%286%29%5E2-4%2A1%2A4=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=20 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+=+%28-6%2B-sqrt%28+20+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-6%2B-sqrt%28+20+%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-%286%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+-0.76393202250021 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%286%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+-0.76393202250021\"   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-%286%29-sqrt%28+20+%29%29%2F2%5C1+=+-5.23606797749979 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%286%29-sqrt%28+20+%29%29%2F2%5C1+=+-5.23606797749979\"   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%2B6x%2B4 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B4\"   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%2B6x%2B4+=+1%28x--0.76393202250021%29%2A%28x--5.23606797749979%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B4+=+1%28x--0.76393202250021%29%2A%28x--5.23606797749979%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.76393202250021, -5.23606797749979.\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%2B6%2Ax%2B4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "#3: Can't tell where your denominators end.  Please<BR>\n" );
document.write( "use parentheses.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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