document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936660>Question 936660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why does a quadratic equation have two answers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570123 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=570123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Why does a quadratic equation have two answers?<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Actually, it doesn't always... <BR>\n" );
document.write( "only if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+b%5E2-4%2Aa%2Ac+%29 ALIGN=MIDDLE  ALT=\"sqrt%28+b%5E2-4%2Aa%2Ac+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > > 0 does it have two 'real' answers... (Blue)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+b%5E2-4%2Aa%2Ac+%29 ALIGN=MIDDLE  ALT=\"sqrt%28+b%5E2-4%2Aa%2Ac+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 , one answer. Ex: y = x^2 (Green)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+b%5E2-4%2Aa%2Ac+%29 ALIGN=MIDDLE  ALT=\"sqrt%28+b%5E2-4%2Aa%2Ac+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0, Imaginary roots only, does not cross x-axis (Purple)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x^2(green),(x-1)^2 -1(Blue), (x-1)^2 +3 (Purple)<BR>\n" );
document.write( "graphically a quadratic equation is a Parabola:<BR>\n" );
document.write( "generally, it will cross the x-axis twice...but not always...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+-10%2C+10%2C+-10%2C+10%2C++grid%281%29%2C%0D%0A%0D%0Agraph%28+300%2C+300%2C++-10%2C+10%2C+-10%2C+10%2C0%2C+x%5E2%2C%28x-1%29%5E2+-1%2C+%28x-1%29%5E2+%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );