document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=11060>Question 11060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> say you have the equation y = x^3 - 3. How would you solve the y-intercept, the x-intercept and the vertex to this equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5796 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=5796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The y-intercept for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E3+-+3 ALIGN=MIDDLE  ALT=\"y+=+x%5E3+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is found by setting x = 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280%29%5E3+-+3 ALIGN=MIDDLE  ALT=\"y+=+%280%29%5E3+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3 ALIGN=MIDDLE  ALT=\"y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > The y-intercept is at (0, -3)\r<BR>\n" );
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document.write( "The vertex? This question would make sense for a quadratic equation, but you have a cubic (third degree) equation and these have no vertex (maximum or minimum).  The best you can do for a cubic function is to find the relative maximum or relative minimum, if there is one.<BR>\n" );
document.write( "Take a look at the grah of this function and you'll see what I mean.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2Cx%5E3-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2Cx%5E3-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can see that the y-intercept is (o, -3) but the vertex?\r<BR>\n" );
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document.write( "Perhaps you meant to type: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+3 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ??\r<BR>\n" );
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document.write( "Let's see what that looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2Cx%5E2-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2Cx%5E2-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-intercept is found, as before, by setting x = 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280%29%5E2+-+3 ALIGN=MIDDLE  ALT=\"y+=+%280%29%5E2+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-intercept is at (0, -3) as you can see on the graph.\r<BR>\n" );
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document.write( "The x-coordinte of the vertex is found by:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%280%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+-%280%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-coordinate of the vertex is found by substituting this value of x into the original equation and solving for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280%29%5E2+-+3 ALIGN=MIDDLE  ALT=\"y+=+%280%29%5E2+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3 ALIGN=MIDDLE  ALT=\"y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-coordinate is y = -3.\r<BR>\n" );
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document.write( "So the vertex is at (0, -3) </SPAN>\n" );
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