document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1709>Question 1709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Where is the vertex of the graph of y=x^2-5. (resubmitted the first person that answered this didn't give the answer) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> quadratics are symmetric about the minimum or maximum point...their shape is either a U-shape (for a positive x^2 term) or is n-shaped (for a negative x^2 term).\r<BR>\n" );
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document.write( "The beauty and ease of finding a quadratic is \"fun\".\r<BR>\n" );
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document.write( "just pick some \"obvious\" points...like\r<BR>\n" );
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document.write( "1. when x=0, then y=-5<BR>\n" );
document.write( "2. when y=0, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=5 ALIGN=MIDDLE  ALT=\"x%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so x HAS 2 SOLUTIONS....+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, we can instantly sketch the graph, and as the curve crosses the x-axis at the \"same\" point on both side of the y-axis, then it is a symmetric shape on the y-axis...so, the minimum point is at y=-5\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-3%2C+3%2C+-6%2C+4%2C+%28x%5E2-5%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-3%2C+3%2C+-6%2C+4%2C+%28x%5E2-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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