document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359435>Question 359435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a quadratic equation in standard form to model the data in the table. \r<BR>\n" );
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document.write( "x	     y<BR>\n" );
document.write( "9	     5<BR>\n" );
document.write( "10	   10<BR>\n" );
document.write( "11	    5<BR>\n" );
document.write( "12	   -10<BR>\n" );
document.write( "13	   -35 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256483 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> standard equation:  y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you need 3 sets of points, any 3 of the 5 sets given will do.<BR>\n" );
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document.write( "This will generate 3 equations in 3 unknowns<BR>\n" );
document.write( "x=9, Y=5  plug this into the standard equation  5=81a+9b+c<BR>\n" );
document.write( "x=10, y=10    plug into std equation   10=100a+10b+c<BR>\n" );
document.write( "x=11, y=5     plug into std equation   5=121a+11b+c<BR>\n" );
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document.write( "eq 1:   5=81a+9b+c<BR>\n" );
document.write( "eq 2:  10=100a+10b+c<BR>\n" );
document.write( "eq 3:  5=121a+11b+c<BR>\n" );
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document.write( "eq 4: 5=19a+b   sub eq1 from eq2 to eliminate c<BR>\n" );
document.write( "eq 5: 0=40a+2b  sub eq1 from eq3 to eliminate c<BR>\n" );
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document.write( "-10=2a   multiply eq4 by -2 and add to eq 5 to eliminate b<BR>\n" );
document.write( "a=-5<BR>\n" );
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document.write( "substitute a=-5 into eq4 or eq5, i'll choose eq 5<BR>\n" );
document.write( "0=40*(-5)+2b<BR>\n" );
document.write( "0=-200+2b<BR>\n" );
document.write( "200=2b<BR>\n" );
document.write( "100=b<BR>\n" );
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document.write( "substitute a=-5, b=100 into one of the 3 original equations, i'll choose eq1<BR>\n" );
document.write( "5=81(-5)+9(100)+c<BR>\n" );
document.write( "5=-405+900+c<BR>\n" );
document.write( "5=495+c<BR>\n" );
document.write( "c=-490<BR>\n" );
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document.write( "a=-5, b=100, c=-490<BR>\n" );
document.write( "substitute into the standard equation<BR>\n" );
document.write( "y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%5E2%2B100x-400 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B100x-400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "validate this equation by choosing a different point<BR>\n" );
document.write( "x=12, y=-10\r<BR>\n" );
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document.write( "-5*(12)^2+100*12-490  does this equal y=-10????<BR>\n" );
document.write( "i'll let you finish this validation\r<BR>\n" );
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document.write( " </SPAN>\n" );
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