document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163024>Question 163024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a graphing problem and it is driving me crazy!!!! It is hard for me to explain it. But I will try. The problem is using a graph of y=-x^2+4x+5 but without solving the equation, or factoring, determing the solution to the equation -x^2+4x+5=0 but we have to use a graph!\r<BR>\n" );
document.write( "\n" );
document.write( "The second problem is, but i'm not sure what is meant by calculate the value of discriminant of x^2+x+3=0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120134 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=120134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B4x%2B5\"   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%2C10%2C-5%2C10%2C-x%5E2%2B4x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-5%2C10%2C-x%5E2%2B4x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the graph, you can see that the parabola crosses the x-axis at x = -1 and x = 5.<BR>\n" );
document.write( "These are the \"zeros\", also known as the solutions, of the equation.<BR>\n" );
document.write( "The \"discriminant\" of a quadratic equation is the quantity under the radical when you use the quadratic formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve.<BR>\n" );
document.write( "So the discriminanat is (<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;\" >)<BR>\n" );
document.write( "In this case, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2B3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now as you can see, the \"discriminant\" is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac+=+1%5E2-4%281%29%283%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+=+1%5E2-4%281%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-12+=+-11 ALIGN=MIDDLE  ALT=\"1-12+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the disciminant is negative which means that the solution to the quadratic equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2B3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have a solution consisting of two complex conjugate roots. In other words, the graph of this equation does not intersect the x-axis. See the graph below:<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%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );