document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039113>Question 1039113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20).  Show your work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653847 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=653847\">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=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > standard form with vertex  (h,k).\r<BR>\n" );
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document.write( "Two of your given points have the same y coordinate for different x coordinates, telling you where the axis of symmetry is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2B4%29%2F2=2%2F2=1 ALIGN=MIDDLE  ALT=\"%28-2%2B4%29%2F2=2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the middle x value of those two points, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You are given a y-intercept, which may give more information for the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%280-1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%280-1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=a%280-1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-4=a%280-1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=a%2Bk ALIGN=MIDDLE  ALT=\"-4=a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What you have found currently is this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%29 ALIGN=MIDDLE  ALT=\"system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Either of the other points should give more information.<BR>\n" );
document.write( "Use  (4,-20),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20=a%284-1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-20=a%284-1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20=9a%2Bk ALIGN=MIDDLE  ALT=\"-20=9a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Summarize again everything found:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%2C9a%2Bk=-20%29 ALIGN=MIDDLE  ALT=\"system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%2C9a%2Bk=-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The two equations here with only variables a and k will permit finding values for a and k.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bk-%289a%2Bk%29=-4-%28-20%29 ALIGN=MIDDLE  ALT=\"a%2Bk-%289a%2Bk%29=-4-%28-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8a=-4%2B20 ALIGN=MIDDLE  ALT=\"-8a=-4%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a=4-20=-16 ALIGN=MIDDLE  ALT=\"8a=4-20=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bk=-4 ALIGN=MIDDLE  ALT=\"a%2Bk=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-4-a ALIGN=MIDDLE  ALT=\"k=-4-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-4-%28-2%29 ALIGN=MIDDLE  ALT=\"k=-4-%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-4%2B2 ALIGN=MIDDLE  ALT=\"k=-4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "EQUATION:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-2%28x-1%29%5E2-2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-2%28x-1%29%5E2-2%29\"   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=graph%28300%2C300%2C-2%2C8%2C-8%2C2%2C-2%28x-1%29%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C8%2C-8%2C2%2C-2%28x-1%29%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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