document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745985>Question 745985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem is to graph the Quadratic Function y= -2Xsquared + 4X+1\r<BR>\n" );
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document.write( "I have tried this problem many times and keep ending up with <BR>\n" );
document.write( "Vertex=(1,-1)<BR>\n" );
document.write( "Y-int=(0,1)<BR>\n" );
document.write( "X-int=(-2.22,0),(.22,0)\r<BR>\n" );
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document.write( "Both x intercepts are to the left of the vertex and the y intercept in in between the two x intercepts, so no symmetric parabola can be graphed.  <BR>\n" );
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document.write( "I am not sure what I am doing wrong, but it probably involved solving for the vertex. I am using the -b/2a formulas and standard x/y int method.  \r<BR>\n" );
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document.write( "Keep in mind, my instructor has written his own workbook, and the equation may have made a mistake.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454098 by </B><A HREF=/tutors/aboutme.mpl?userid=savvyhush23><B>savvyhush23(50)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=savvyhush23><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=savvyhush23><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First solve the equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%5E2+%2B+4x%2B1 ALIGN=MIDDLE  ALT=\"y=-2x%5E2+%2B+4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the squared term is x, equate the system in x, thus,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-4x%2By-1=0 ALIGN=MIDDLE  ALT=\"2x%5E2-4x%2By-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, completing the square<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-4x%2B2%2By-1=2 ALIGN=MIDDLE  ALT=\"2x%5E2-4x%2B2%2By-1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, add two both side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-2x%2B1%29=-y%2B3 ALIGN=MIDDLE  ALT=\"2%28x%5E2-2x%2B1%29=-y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-1%29%5E2=%28-1%2F2%29%28y-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-1%29%5E2=%28-1%2F2%29%28y-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The parabola is facing downward,<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=-2x%5E2%2B4x%2B1+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B4x%2B1+=+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=%284%29%5E2-4%2A-2%2A1=24 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A-2%2A1=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=24 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+=+%28-4%2B-sqrt%28+24+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+24+%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-%284%29%2Bsqrt%28+24+%29%29%2F2%5C-2+=+-0.224744871391589 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+24+%29%29%2F2%5C-2+=+-0.224744871391589\"   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-%284%29-sqrt%28+24+%29%29%2F2%5C-2+=+2.22474487139159 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%284%29-sqrt%28+24+%29%29%2F2%5C-2+=+2.22474487139159\"   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=-2x%5E2%2B4x%2B1 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B4x%2B1\"   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=-2x%5E2%2B4x%2B1+=+-2%28x--0.224744871391589%29%2A%28x-2.22474487139159%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B4x%2B1+=+-2%28x--0.224744871391589%29%2A%28x-2.22474487139159%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.224744871391589, 2.22474487139159.\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+-2%2Ax%5E2%2B4%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B4%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( ".<BR>\n" );
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document.write( "so, the vertex:(1,3)<BR>\n" );
document.write( "x-intercept: (-2.22,0),(0.22,0)<BR>\n" );
document.write( "y-intercept: (0,1) </SPAN>\n" );
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