document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006597>Question 1006597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given g(x) = 1/(4(x-5)^2 -1). For what value of x is function g undefined?\r<BR>\n" );
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document.write( "My attempt: I take this to mean \"for what value of x does the denominator = 0.\" Assuming that's correct, I set the denominator equal to 0. I get a quadratic equation. I plug the coefficients into the quadratic formula, but I do NOT get the correct answer, which is supposed to equal 4 and 1/2.\r<BR>\n" );
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document.write( "I think I'm not doing the order of operations right in converting the denominator into the quadratic formula.\r<BR>\n" );
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document.write( "I won't belabor you with all my different attempts. Could someone show me how the math should go? The other answer choices are 5 and 1/4, 5, and 1. I did get to 5 and 1/4, but I do think that's wrong mathematically.\r<BR>\n" );
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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 #622726 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=622726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There's no need to use the quadratic formula since that would require us to expand/simplify the left side. It's more work than needed in my opinion.\r<BR>\n" );
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document.write( "Since it's in vertex form, we can isolate x to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-5%29%5E2+-1=0 ALIGN=MIDDLE  ALT=\"4%28x-5%29%5E2+-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-5%29%5E2+-1%2B1=0%2B1 ALIGN=MIDDLE  ALT=\"4%28x-5%29%5E2+-1%2B1=0%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-5%29%5E2=1 ALIGN=MIDDLE  ALT=\"4%28x-5%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A4%28x-5%29%5E2=%281%2F4%29%2A1 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2A4%28x-5%29%5E2=%281%2F4%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 1/4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2=1%2F4 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-5%29%5E2%29=sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-5%29%5E2%29=sqrt%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the square root to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29=sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"abs%28x-5%29=sqrt%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29+=+abs%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29+=+abs%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is any real number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=1%2F2 ALIGN=MIDDLE  ALT=\"x-5=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=-1%2F2 ALIGN=MIDDLE  ALT=\"x-5=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Split up the absolute value into the plus/minus components\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2B5=1%2F2%2B5 ALIGN=MIDDLE  ALT=\"x-5%2B5=1%2F2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2B5=-1%2F2%2B5 ALIGN=MIDDLE  ALT=\"x-5%2B5=-1%2F2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > For each equation, add 5 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1%2F2%2B10%2F2 ALIGN=MIDDLE  ALT=\"x+=+1%2F2%2B10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F2%2B10%2F2 ALIGN=MIDDLE  ALT=\"x+=+-1%2F2%2B10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11%2F2 ALIGN=MIDDLE  ALT=\"x+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%2F2 ALIGN=MIDDLE  ALT=\"x+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the two solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-5%29%5E2+-1=0 ALIGN=MIDDLE  ALT=\"4%28x-5%29%5E2+-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11%2F2 ALIGN=MIDDLE  ALT=\"x+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%2F2 ALIGN=MIDDLE  ALT=\"x+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So g(x) is undefined when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11%2F2 ALIGN=MIDDLE  ALT=\"x+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%2F2 ALIGN=MIDDLE  ALT=\"x+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Side Notes: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%26+1%2F2+=+9%2F2 ALIGN=MIDDLE  ALT=\"4+%26+1%2F2+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%26+1%2F2+=+11%2F2 ALIGN=MIDDLE  ALT=\"5+%26+1%2F2+=+11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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