document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177348>Question 177348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me answer this question?\r<BR>\n" );
document.write( "\n" );
document.write( "If you are looking at a graph of a quadratic equation, how do\r<BR>\n" );
document.write( "\n" );
document.write( "you determine where the solutions are? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132412 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=132412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The \"solutions\" or \"roots\" to a quadratic equation are the points on the graph of the equation where the graph (a parabola) intersects the x-axis.<BR>\n" );
document.write( "Of course, some parabolas will intersect the x-axis in two places (1st. graph) in which case the equation is said to have two real roots.<BR>\n" );
document.write( "Some parabolas will have their vertex just touching the x-axis (2nd graph).  Such an equation is said to have double root or two identical roots.<BR>\n" );
document.write( "Other parabolas will not intersect the x-axis at all (3rd graph), in which case, the equation is said to have no real roots.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C8%2C-5%2C5%2Cx%5E2-5x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C8%2C-5%2C5%2Cx%5E2-5x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B4x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Bx%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Bx%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );