document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242588>Question 242588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you can find this you must be a genius! I've been working on this for half an hour... I would greatly appreciate it!<BR>\n" );
document.write( "y=6x^2-9x-13<BR>\n" );
document.write( "What is the larger intercept? What is the smaller intercept? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177598 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 6x^2 -9x - 13\r<BR>\n" );
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document.write( "a = 6<BR>\n" );
document.write( "b = -9<BR>\n" );
document.write( "c = -13\r<BR>\n" );
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document.write( "b^2 - 4ac = 81 - (4*6*(-13) = 81 + 312 = 393\r<BR>\n" );
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document.write( "393 is not a perfect square so the answer will not be an integer.\r<BR>\n" );
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document.write( "quadratic formula is required or completing the square.   we'll use quadratic formula.\r<BR>\n" );
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document.write( "x = (-b +/- sqrt(b^2-4ac))/(2a)\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "(-(-9) +/- sqrt(393))/12 which becomes:\r<BR>\n" );
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document.write( " (9 +/- sqrt(393))/12 which becomes:\r<BR>\n" );
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document.write( "x = -.902018967\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "x = 2.402018967\r<BR>\n" );
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document.write( "a graph of your equation looks like this:\r<BR>\n" );
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document.write( "I'm not a genius.\r<BR>\n" );
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document.write( "I just used the quadratic formula which works every time whether or not you have real roots.\r<BR>\n" );
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document.write( "if you can't factor the equation, then use the quadratic formula.\r<BR>\n" );
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document.write( "this one could not be factored because the discriminant (b^2-4ac) was not a perfect square.\r<BR>\n" );
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document.write( "if b^2-4ac was negative you would not have any real roots because square root of a negative number doesn't yield real roots.\r<BR>\n" );
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document.write( "if b^2 - 4ac was equal to 0, you would have only one root.\r<BR>\n" );
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document.write( "if b^2 - 4ac was positive, you would have two real roots (your problem fits this).\r<BR>\n" );
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document.write( "if b^2 - 4ax was positive and a perfect square, you would have real roots that are integers.\r<BR>\n" );
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document.write( "standard form of quadratic equation is:\r<BR>\n" );
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document.write( "ax^2 + bx + c\r<BR>\n" );
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document.write( "a is the coefficient of the x^2 term.<BR>\n" );
document.write( "b is the coefficient of the x term.<BR>\n" );
document.write( "c is the constant.\r<BR>\n" );
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document.write( "your equation was 6x^2 - 9x - 13\r<BR>\n" );
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document.write( "that made a = 6, b = -9, c = -13\r<BR>\n" );
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document.write( " </SPAN>\n" );
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