document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143907>Question 143907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tutors...HELP...Thank you<BR>\n" );
document.write( "find an equation of  the inverse relation y=3x^2-5x+9\r<BR>\n" );
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document.write( "x=1/2y+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104725 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=104725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3+x%5E2-5+x%2B9 ALIGN=MIDDLE  ALT=\"y=3+x%5E2-5+x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=3+x%5E2-5+x ALIGN=MIDDLE  ALT=\"y-9=3+x%5E2-5+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=3%28x%5E2%2B%28-5%2F3%29x%29 ALIGN=MIDDLE  ALT=\"y-9=3%28x%5E2%2B%28-5%2F3%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take half of the x coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F6 ALIGN=MIDDLE  ALT=\"-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28-5%2F3%29=-5%2F6 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-5%2F3%29=-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F6 ALIGN=MIDDLE  ALT=\"-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F36 ALIGN=MIDDLE  ALT=\"25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2F6%29%5E2=%28-5%2F6%29%28-5%2F6%29=25%2F36 ALIGN=MIDDLE  ALT=\"%28-5%2F6%29%5E2=%28-5%2F6%29%28-5%2F6%29=25%2F36\"   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=y-9=3%28x%5E2%2B%28-5%2F3%29x%2B25%2F36-25%2F36%29 ALIGN=MIDDLE  ALT=\"y-9=3%28x%5E2%2B%28-5%2F3%29x%2B25%2F36-25%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F36 ALIGN=MIDDLE  ALT=\"25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not change the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=3%28%28x-5%2F6%29%5E2-25%2F36%29 ALIGN=MIDDLE  ALT=\"y-9=3%28%28x-5%2F6%29%5E2-25%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28-5%2F3%29x%2B25%2F36 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28-5%2F3%29x%2B25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%2F6%29%5E2\"   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=y-9=3%28x-5%2F6%29%5E2-3%2825%2F36%29 ALIGN=MIDDLE  ALT=\"y-9=3%28x-5%2F6%29%5E2-3%2825%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-9=3%28x-5%2F6%29%5E2-25%2F12 ALIGN=MIDDLE  ALT=\"y-9=3%28x-5%2F6%29%5E2-25%2F12\"   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=y=3%28x-5%2F6%29%5E2-25%2F12%2B9 ALIGN=MIDDLE  ALT=\"y=3%28x-5%2F6%29%5E2-25%2F12%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x-5%2F6%29%5E2%2B83%2F12 ALIGN=MIDDLE  ALT=\"y=3%28x-5%2F6%29%5E2%2B83%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now the quadratic is in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%28y-5%2F6%29%5E2%2B83%2F12 ALIGN=MIDDLE  ALT=\"x=3%28y-5%2F6%29%5E2%2B83%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch x and y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-83%2F12=3%28y-5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"x-83%2F12=3%28y-5%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83%2F12 ALIGN=MIDDLE  ALT=\"83%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-83%2F12%29%2F3=%28y-5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-83%2F12%29%2F3=%28y-5%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F3-%2883%2F12%29%2F3=%28y-5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%2F3-%2883%2F12%29%2F3=%28y-5%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F3-83%2F36=%28y-5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%2F3-83%2F36=%28y-5%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide and reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B-sqrt%28%28x%29%2F3-83%2F36%29=y-5%2F6 ALIGN=MIDDLE  ALT=\"0%2B-sqrt%28%28x%29%2F3-83%2F36%29=y-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B-sqrt%28%28x%29%2F3-83%2F36%29%2B5%2F6=y ALIGN=MIDDLE  ALT=\"0%2B-sqrt%28%28x%29%2F3-83%2F36%29%2B5%2F6=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "So the inverse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%2B-sqrt%28%28x%29%2F3-83%2F36%29%2B5%2F6 ALIGN=MIDDLE  ALT=\"y=0%2B-sqrt%28%28x%29%2F3-83%2F36%29%2B5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F2%29y%2B4 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=%281%2F2%29y ALIGN=MIDDLE  ALT=\"x-4=%281%2F2%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-4%29=y ALIGN=MIDDLE  ALT=\"2%28x-4%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-8=y ALIGN=MIDDLE  ALT=\"2x-8=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So the inverse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-8 ALIGN=MIDDLE  ALT=\"y=2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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