document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118946>Question 118946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation is given by y=2x^2 - 6bx+3.What is the value of 'b' if the equation of the axis of symmetry is x=9 ? I think the answer is 6 but I really don't fully understand, can someone please explain this to me ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87066 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=87066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the axis of symmetry, take the x coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6b ALIGN=MIDDLE  ALT=\"-6b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and divide it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2 ALIGN=MIDDLE  ALT=\"2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and negate it. Remember, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2+-+6bx%2B3 ALIGN=MIDDLE  ALT=\"y=2x%5E2+-+6bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the axis of symmetry is <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;\" >. So in our case,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28-6b%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x=-%28-6b%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the axis of symmetry is x=9, this means \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-%28-6b%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"9=-%28-6b%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=6b%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"9=6b%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -6b\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=6b%2F4 ALIGN=MIDDLE  ALT=\"9=6b%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=6b ALIGN=MIDDLE  ALT=\"36=6b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=b ALIGN=MIDDLE  ALT=\"6=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6\r<BR>\n" );
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document.write( "So our answer is <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;\" >. So you are correct.\r<BR>\n" );
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document.write( "If we plug in <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;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2+-+6bx%2B3 ALIGN=MIDDLE  ALT=\"y=2x%5E2+-+6bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2+-+6%286%29x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%5E2+-+6%286%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2+-+36x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%5E2+-+36x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Now let's graph\r<BR>\n" );
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document.write( "So we can see that the axis of symmetry is x=9. So this verifies our answer. </SPAN>\n" );
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