document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6736>Question 6736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can somebody show me how to find the coordinates of the vertex of the graph of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E2-6x%2B2+ ALIGN=MIDDLE  ALT=\"+2%5E2-6x%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3716 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=3716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several ways to find the coordinates of the vertex of a parabola.\r<BR>\n" );
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document.write( "I'm assuming that there is a typographical error in your question.\r<BR>\n" );
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document.write( "You probably meant to type:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+6x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+6x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If not, your question is meaningless.\r<BR>\n" );
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document.write( "If this is the equation you intended, then read on.\r<BR>\n" );
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document.write( "1)  You could graph the equation and find the location of the vertex of the parabola, or\r<BR>\n" );
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document.write( "2) You could put the equation into the form:  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and read the coordinates of the vertex from: (h, k)<BR>\n" );
document.write( "This method requires that you perform an operation known as \"completing the square\".\r<BR>\n" );
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document.write( "3) You could put your equation into standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then find the x-coordinate of the vertex which is located at -b/2a.<BR>\n" );
document.write( "Then you could get the y-coordinate by substituting the x-value into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-+6x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-+6x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for y.\r<BR>\n" );
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document.write( "Here's method 2.<BR>\n" );
document.write( "Set you equation equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 2 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+=+-2 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add the square of half the x-coefficient (-3)^2 = 9 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+%2B+9+=+7 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+%2B+9+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%28x+-+3%29+=+7 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%28x+-+3%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add 7 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%5E2+-+7+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%5E2+-+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  You now have the equation in the a(x-h)^2 + k form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >  h = 3 and k = -7\r<BR>\n" );
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document.write( "The coordinates of the vertex are: (h, k) or (3, -7)\r<BR>\n" );
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