document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185936>Question 185936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I seem to be having problems with the graphing portions. I never know what the graph is going to look like based on the equation. For example, y=(3x^2+4x+4)/(x^2-5x-6). With this problem, I need to find the x-intercepts, the vertical asymptote and (if applicable) the horizontal asymptote. Could you please help me solve this problem? Is there a trick to knowing what general shape your graph will have depending on the equation?<BR>\n" );
document.write( "Thank you for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139418 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=139418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=(3x^2+4x+4)/(x^2-5x-6). With this problem, <BR>\n" );
document.write( "I need to find the x-intercepts,<BR>\n" );
document.write( "Let y = 0 and solve for \"x\":<BR>\n" );
document.write( "(3x^2+4x+4)/(x^2-5x-6)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The fraction is zero when the numerator is zero:<BR>\n" );
document.write( "Solve 3x^2 + 4x + 4 = 0 using the quadratic formula:<BR>\n" );
document.write( "x = [-4 +- sqrt(16 - 4*3*4)]/6<BR>\n" );
document.write( "16-48 is negative so there are no Real Number solutions; no x-intercepts<BR>\n" );
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document.write( " <BR>\n" );
document.write( "the vertical asymptote <BR>\n" );
document.write( "---<BR>\n" );
document.write( "You have vertical asymptotes when the denominator is zero and the numerator is not zero.<BR>\n" );
document.write( "Solve x^2-5x-6 = 0<BR>\n" );
document.write( "(x-6)(x+1) = 0<BR>\n" );
document.write( "x = 6 and x=-1 are vertical asymptotes<BR>\n" );
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document.write( "the horizontal asymptote of y=(3x^2+4x+4)/(x^2-5x-6) <BR>\n" );
document.write( "y = 3x^2/x^2 = 3 is the horizontal asymptote\r<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------<BR>\n" );
document.write( " Is there a trick to knowing what general shape your graph will have depending on the equation?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "There is no trick.  That is why you find the intercepts and the asymptotes.<BR>\n" );
document.write( "That way you have a general idea what the graph looks like.<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Graph: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-20%2C30%2C%283x%5E2%2B4x%2B4%29%2F%28x%5E2-5x-6%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-20%2C30%2C%283x%5E2%2B4x%2B4%29%2F%28x%5E2-5x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------------------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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