document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815212>Question 815212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For which value of b will the quadratic function below have an x-value of 6 at the minimum ? \r<BR>\n" );
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document.write( "f(x)=x^2-2bx+7 \r<BR>\n" );
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document.write( "Any help will be great, thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490769 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=490769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F2a+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when the form of the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+-+2b%2Ax+%2B+7+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+-+2b%2Ax+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-2b+ ALIGN=MIDDLE  ALT=\"+b+=+-2b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( different b's )<BR>\n" );
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document.write( "So, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+6+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+=+%28-%28-2b%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+6+=+%28-%28-2b%29%29+%2F+%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+=+%282b%29%2F2+ ALIGN=MIDDLE  ALT=\"+6+=+%282b%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=+2b+=+12+ ALIGN=MIDDLE  ALT=\"+2b+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+6+ ALIGN=MIDDLE  ALT=\"+b+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "So, the equation would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+-+2%2A6%2Ax+%2B+7+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+-+2%2A6%2Ax+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+-+12x+%2B+7+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+-+12x+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+15%2C+-30%2C+5%2C+x%5E2+-+12x+%2B+7+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+15%2C+-30%2C+5%2C+x%5E2+-+12x+%2B+7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=6+ ALIGN=MIDDLE  ALT=\"+x=6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=-29+ ALIGN=MIDDLE  ALT=\"+y=-29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or so<BR>\n" );
document.write( "I'll check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+-+12x+%2B+7+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+-+12x+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+6%5E2+-12%2A6+%2B+7+ ALIGN=MIDDLE  ALT=\"+y+=+6%5E2+-12%2A6+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+36+-+72+%2B+7+ ALIGN=MIDDLE  ALT=\"+y+=+36+-+72+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-29+ ALIGN=MIDDLE  ALT=\"+y+=+-29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );