document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878392>Question 878392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16.   Which quadratic rule represents the data in the table?<BR>\n" );
document.write( "x -1,0,1,2,3<BR>\n" );
document.write( "y 6,5,6,9,14  this is what the data looks like\r<BR>\n" );
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document.write( "y = –2x² + 5<BR>\n" );
document.write( "y = –x² + 5<BR>\n" );
document.write( "y = x² – 5<BR>\n" );
document.write( "y = x² + 5\r<BR>\n" );
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document.write( "I think it is b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #529928 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=529928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Why do you think it is b?\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ -x^2\ +\ 5\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(-1)\ =\ -(-1)^2\ +\ 5\ =\ -1\ +\ 5\ =\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(0)\ =\ -(0)^2\ +\ 5\ =\ 0\ +\ 5\ =\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(1)\ =\ -(1)^2\ +\ 5\ =\ -1\ +\ 5\ =\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(2)\ =\ -(2)^2\ +\ 5\ =\ -4\ +\ 5\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(3)\ =\ -(3)^2\ +\ 5\ =\ -9\ +\ 5\ =\ -4\">\r<BR>\n" );
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document.write( "So apparently b is incorrect.\r<BR>\n" );
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document.write( "Consider the standard form of a quadratic function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "If the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-1, 6)\"> is an element of the solution set, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6\ =\ a(-1)^2\ +\ b(-1)\ +\ c\"> must hold and\r<BR>\n" );
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document.write( "If the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (0, 5)\"> is an element of the solution set, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5\ =\ a(0)^2\ +\ b(0)\ +\ c\"> must hold and\r<BR>\n" );
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document.write( "If the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (1, 6)\"> is an element of the solution set, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6\ =\ a(1)^2\ + b(1)\ +\ c\"> must hold.\r<BR>\n" );
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document.write( "Simplfying:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ -\ b\ +\ c\ =\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\ =\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ b\ +\ c\ =\ 6\">\r<BR>\n" );
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document.write( "Substituting\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ -\ b\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ b\ =\ 1\">\r<BR>\n" );
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document.write( "Solving by elimination:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ =\ 1\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 0\">\r<BR>\n" );
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document.write( "Substituting the now known values of a, b, and c into <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large ax^2\ +\ bx\ +\ c\"> yields:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ x^2\ +\ 5\">\r<BR>\n" );
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document.write( "Checking the result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(-1)\ =\ (-1)^2\ +\ 5\ =\ 1\ +\ 5\ =\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(0)\ =\ (0)^2\ +\ 5\ =\ 0\ +\ 5\ =\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(1)\ =\ (1)^2\ +\ 5\ =\ 1\ +\ 5\ =\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(2)\ =\ (2)^2\ +\ 5\ =\ 4\ +\ 5\ =\ 9\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(3)\ =\ (3)^2\ +\ 5\ =\ 9\ +\ 5\ =\ 14\">\r<BR>\n" );
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document.write( "Looks right to me.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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