document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443092>Question 443092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the eqaution of the parabola given the three points: (1,0),(0,-4),(2,6)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305634 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that<BR>\n" );
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document.write( "0 = a + b +c<BR>\n" );
document.write( "-4 = 0 + 0 + c<BR>\n" );
document.write( "6 = 4a + 2b +c<BR>\n" );
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document.write( "we know c = -4<BR>\n" );
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document.write( "0 = a+b-4<BR>\n" );
document.write( "6 = 4a +2b -4<BR>\n" );
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document.write( "a + b = 4<BR>\n" );
document.write( "4a + 2b = 10\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Ca+%2B+1%5Cb+=+4%2C%0D%0A++++4%5Ca+%2B+2%5Cb+=+10+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Ca+%2B+1%5Cb+=+4%2C%0D%0A++++4%5Ca+%2B+2%5Cb+=+10+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*b to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Aa+=+4+-+1%2Ab ALIGN=MIDDLE  ALT=\"1%2Aa+=+4+-+1%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4%2F1+-+1%2Ab%2F1 ALIGN=MIDDLE  ALT=\"a+=+4%2F1+-+1%2Ab%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%284%2F1+-+1%2Ab%2F1%29+%2B+2%5Cb+=+10 ALIGN=MIDDLE  ALT=\"4%2A%284%2F1+-+1%2Ab%2F1%29+%2B+2%5Cb+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that b=3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4%2F1+-+1%2Ab%2F1 ALIGN=MIDDLE  ALT=\"a+=+4%2F1+-+1%2Ab%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a=1.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+a=1%2C+b=3+%29 ALIGN=MIDDLE  ALT=\"system%28+a=1%2C+b=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So a = 1 b = 3 c =-4\r<BR>\n" );
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document.write( "So our quadratic is x^2 + 3x - 4\r<BR>\n" );
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