document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178755>Question 1178755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a system of linear equations to find the quadratic function <BR>\n" );
document.write( "f(x) = ax2 + bx + c<BR>\n" );
document.write( " that satisfies the given conditions. Solve the system using matrices.<BR>\n" );
document.write( "f(1) = 9, f(2) = 10, f(3) = 9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808157 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=808157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that satisfies the given conditions. Solve the system using matrices.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+9 ALIGN=MIDDLE  ALT=\"f%281%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=+10 ALIGN=MIDDLE  ALT=\"f%282%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+9 ALIGN=MIDDLE  ALT=\"f%283%29+=+9\"   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+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+9 ALIGN=MIDDLE  ALT=\"f%281%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+9 ALIGN=MIDDLE  ALT=\"f%28x%29+=+9\"   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=9+=+a%2A1%5E2+%2B+b%2A1+%2B+c ALIGN=MIDDLE  ALT=\"9+=+a%2A1%5E2+%2B+b%2A1+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+%2B+c=9 ALIGN=MIDDLE  ALT=\"+a+%2B+b+%2B+c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29+=10 ALIGN=MIDDLE  ALT=\"f%282%29+=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+10 ALIGN=MIDDLE  ALT=\"f%28x%29+=+10\"   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=10+=+a%2A2%5E2+%2B+b%2A2+%2B+c ALIGN=MIDDLE  ALT=\"10+=+a%2A2%5E2+%2B+b%2A2+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+%2B+2b+%2B+c=10 ALIGN=MIDDLE  ALT=\"+4a+%2B+2b+%2B+c=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >...................eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=9 ALIGN=MIDDLE  ALT=\"f%283%29+=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+9 ALIGN=MIDDLE  ALT=\"f%28x%29+=+9\"   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=9+=+a%2A3%5E2+%2B+b%2A3+%2B+c ALIGN=MIDDLE  ALT=\"9+=+a%2A3%5E2+%2B+b%2A3+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9a+%2B+3b+%2B+c=9 ALIGN=MIDDLE  ALT=\"+9a+%2B+3b+%2B+c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................eq.3\r<BR>\n" );
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document.write( "your system is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+b+%2B+c=9 ALIGN=MIDDLE  ALT=\"+a+%2B+b+%2B+c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+%2B+2b+%2B+c=10 ALIGN=MIDDLE  ALT=\"+4a+%2B+2b+%2B+c=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >...................eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9a+%2B+3b+%2B+c=9 ALIGN=MIDDLE  ALT=\"+9a+%2B+3b+%2B+c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................eq.3<BR>\n" );
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document.write( "Your matrix\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%091%2C%091%2C%099%2C%0D%0A4%2C%092%2C%091%2C%0910%2C%0D%0A9%2C%093%2C%091%2C%099%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 1st column in the 1st row\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%091%2C%091%2C%099%2C%0D%0A4%2C%092%2C%091%2C%0910%2C%0D%0A9%2C%093%2C%091%2C%099%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 1st column\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%091%2C%091%2C%099%2C%0D%0A0%2C%09-2%2C%09-3%2C%09-26%2C%0D%0A0%2C%09-6%2C%09-8%2C%09-72%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A%0D%0A1%2C%091%2C%091%2C%099%2C%0D%0A0%2C%091%2C%093%2F2%2C%0913%2C%0D%0A0%2C%09-6%2C%09-8%2C%09-72%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 2nd column\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%090%2C%09-1%2F2%2C%09-4%2C%0D%0A0%2C%091%2C%093%2F2%2C%0913%2C%0D%0A0%2C%090%2C%091%2C%096%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 3rd column in the 3rd row\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%090%2C%09-1%2F2%2C%09-4%2C%0D%0A0%2C%091%2C%093%2F2%2C%0913%2C%0D%0A0%2C%090%2C%091%2C%096%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 3rd column\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2C%0D%0A1%2C%090%2C%090%2C%09-1%2C%0D%0A0%2C%091%2C%090%2C%094%2C%0D%0A0%2C%090%2C%091%2C%096%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution set:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4 ALIGN=MIDDLE  ALT=\"b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+6 ALIGN=MIDDLE  ALT=\"c+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the quadratic function is:\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+%2B+4x+%2B+6 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-x%5E2+%2B+4x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );