document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084125>Question 1084125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the square to write each function in f(x) = a(x-h)^2 + k form. Determine the vertex and the axis of symmetry of the graph of the function. Then plot several points to complete the graph. \r<BR>\n" );
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document.write( "f(x) = x^2 - x - 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698188 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=698188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Complete the square to write each function in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > form. Determine the vertex and the axis of symmetry of the graph of the function. <BR>\n" );
document.write( "Then plot several points to complete the graph. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2+-+x+-+6 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2+-+x+-+6\"   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=f%28x%29+=%28x%5E2+-+x+%2Bb%5E2%29-b%5E2-+6 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x%5E2+-+x+%2Bb%5E2%29-b%5E2-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=-1 ALIGN=MIDDLE  ALT=\"2ab=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can determine <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=2ab=-1 ALIGN=MIDDLE  ALT=\"2ab=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=-1 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=-1 ALIGN=MIDDLE  ALT=\"2b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1%2F2 ALIGN=MIDDLE  ALT=\"b=-1%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=f%28x%29+=%28x%5E2+-+x+%2B%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2-+6 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x%5E2+-+x+%2B%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2-+6\"   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=f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+6 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+6\"   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=f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+24%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+24%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=f%28x%29+=%28x+-1%2F2%29%5E2-25%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x+-1%2F2%29%5E2-25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1%2F2 ALIGN=MIDDLE  ALT=\"h=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-25%2F4 ALIGN=MIDDLE  ALT=\"k=-25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25%2F4 ALIGN=MIDDLE  ALT=\"-25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)&#8776;(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5 ALIGN=MIDDLE  ALT=\"0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6.25 ALIGN=MIDDLE  ALT=\"-6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The axis of symmetry of a parabola is the vertical line through the vertex.\r<BR>\n" );
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document.write( "so, axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.5 ALIGN=MIDDLE  ALT=\"x=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "table:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29+=+%28-2%29%5E2+-+%28-2%29-+6=4%2B2-6=0 ALIGN=MIDDLE  ALT=\"f%28-2%29+=+%28-2%29%5E2+-+%28-2%29-+6=4%2B2-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+%28-1%29%5E2+-+%28-1%29-+6=1%2B1-6=-4 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+%28-1%29%5E2+-+%28-1%29-+6=1%2B1-6=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+%280%29%5E2+-+%280%29-+6=0%2B0-6=-6 ALIGN=MIDDLE  ALT=\"f%280%29+=+%280%29%5E2+-+%280%29-+6=0%2B0-6=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+%281%29%5E2+-+%281%29-+6=1-1-6=-6 ALIGN=MIDDLE  ALT=\"f%281%29+=+%281%29%5E2+-+%281%29-+6=1-1-6=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+%282%29%5E2+-+%282%29-+6=4-2-6=-4 ALIGN=MIDDLE  ALT=\"f%282%29+=+%282%29%5E2+-+%282%29-+6=4-2-6=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "plot points and draw a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%280.5%2C-6.25%2C.12%29%2Clocate%280.5%2C-6.35%2CV%280.5%2C-6.25%29%29%2C%0D%0Acircle%28-2%2C0%2C.12%29%2Clocate%28-2.2%2C0.6%2Cp%28-2%2C0%29%29%2C%0D%0Acircle%28-1%2C-4%2C.12%29%2Clocate%28-1%2C-4%2Cp%28-1%2C-4%29%29%2C%0D%0Acircle%280%2C-6%2C.12%29%2Clocate%280.2%2C-6%2Cp%280%2C-6%29%29%2C%0D%0Acircle%281%2C-6%2C.12%29%2Clocate%281%2C-6%2Cp%281%2C-6%29%29%2C%0D%0Acircle%282%2C-4%2C.12%29%2Clocate%282%2C-4%2Cp%282%2C-4%29%29%2C%0D%0Aline%281%2F2%2C-10%2C1%2F2%2C10%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+x+-+6%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );