document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142976>Question 142976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Solve   by completing the square.  Find exact solutions.  Then:<BR>\n" );
document.write( "a.	Find the vertex.<BR>\n" );
document.write( "b.	Find the line of symmetry.<BR>\n" );
document.write( "c.	Determine whether there is a maximum or minimum value and find that value.<BR>\n" );
document.write( "d.	Show a sketch of the graph.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104027 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=104027\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x=18 ALIGN=MIDDLE  ALT=\"x%5E2-3x=18\"   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%5E2-3x%2B9%2F4=18%2B9%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B9%2F4=18%2B9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the x coefficient 3 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Add this number 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%5E2-3x%2B9%2F4=81%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B9%2F4=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 18 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F4 ALIGN=MIDDLE  ALT=\"81%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=%28x-3%2F2%29%5E2=81%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side. Now the left side is a complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%2F2=0%2B-sqrt%2881%2F4%29 ALIGN=MIDDLE  ALT=\"x-3%2F2=0%2B-sqrt%2881%2F4%29\"   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=x-3%2F2=9%2F2 ALIGN=MIDDLE  ALT=\"x-3%2F2=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%2F2=-9%2F2 ALIGN=MIDDLE  ALT=\"x-3%2F2=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and expand\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9%2F2%2B3%2F2 ALIGN=MIDDLE  ALT=\"x=9%2F2%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-9%2F2%2B3%2F2 ALIGN=MIDDLE  ALT=\"x=-9%2F2%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides in each case\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12%2F2 ALIGN=MIDDLE  ALT=\"x=12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6%2F2 ALIGN=MIDDLE  ALT=\"x=-6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the solutions are <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2=81%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2=81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the completed square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2-81%2F4=0 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2-81%2F4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F4 ALIGN=MIDDLE  ALT=\"81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "Now the equation is in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the vertex is (h,k)\r<BR>\n" );
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document.write( "So in this case, the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{3}{2},-\frac{81}{4}\right)\">\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "The line of symmetry is simply the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=h ALIGN=MIDDLE  ALT=\"x=h\"   DISABLED_style= \"max-width:90%; height:auto;\" > where h is the x-coordinate of the vertex. So the axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "Remember, we're still using the general form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2-81%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2-81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <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;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the parabola opens up and there is a minimum. So the minimum occurs at the vertex which means that the minimum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-81%2F4 ALIGN=MIDDLE  ALT=\"-81%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d) \r<BR>\n" );
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document.write( "Finally here's a sketch to visually verify our answers\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-20%2C20%2C-22%2C22%2C%28x-3%2F2%29%5E2-81%2F4%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-20%2C20%2C-22%2C22%2C%28x-3%2F2%29%5E2-81%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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