document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=308536>Question 308536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, <BR>\n" );
document.write( "I am trying to solve quadratic equations by graphing, I have been looking at the example of the book and makes no sence to me.<BR>\n" );
document.write( "the problem is asking me to use a graph to estimate the solutions of the equation, and to check my solutions algebraically.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x%5E2-8x=12+ ALIGN=MIDDLE  ALT=\"+-4x%5E2-8x=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #220610 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=220610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use a graph to estimate the solutions of the equation, and to check my solutions algebraically.\r<BR>\n" );
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document.write( "-4x^2-8x=12 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Divide thru by -4 to simplify the equation.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + 2x = -3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Graph the two equations<BR>\n" );
document.write( "y = x^2+2x<BR>\n" );
document.write( "and <BR>\n" );
document.write( "y = -3<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B2x%2C-3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B2x%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Find the points of intersection of the two graphs.<BR>\n" );
document.write( "Note: The graphs do not intersect; there is no Real<BR>\n" );
document.write( "Number solutions for the problem.<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "Solving analytically:<BR>\n" );
document.write( "x^2 + 2x +3 = 0<BR>\n" );
document.write( "x = [-2 +- sqrt(4 -4*3)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = [-2 +- sqrt(-8)]/2<BR>\n" );
document.write( "x = [-2 +-2isqrt(2)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = [-1 +- isqrt(2)]<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Note: These solutions are complex numbers.<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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