document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=560249>Question 560249</A>: <I><SPAN STYLE=\"word-break: break-all;\">   How do you create a quadratic equation with only one solution?  What does it mean to only have one solution for a quadratic equation? \r<BR>\n" );
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document.write( "The solution for my quadratic equation is -2.  Please determine the quadratic equation and show all of your steps </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363823 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a quadratic equation has solutions, the quadratic expression part of the equation can be written as a product of two binomial factors and a number<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=a%28x-m%29%28x-n%29 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=a%28x-m%29%28x-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-m%29%28x-n%29=0 ALIGN=MIDDLE  ALT=\"a%28x-m%29%28x-n%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the solutions.<BR>\n" );
document.write( "When those solutions are integers, you may be able to solve the equation by factoring.<BR>\n" );
document.write( "If the two solutions are the same, you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-m%29%5E2=0 ALIGN=MIDDLE  ALT=\"a%28x-m%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That formula represents all the quadratic equations that have only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a solution. There are infinitely many of them, because there are infitely many values that you can choose for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2 ALIGN=MIDDLE  ALT=\"m=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-m%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-m%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-2%29%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-%28-2%29%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and is equivalent to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is probably the expected answer.<BR>\n" );
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