document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331817>Question 331817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please use the standard from of a parabola given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > to write an eqaution of a parabola that passes through the given points<BR>\n" );
document.write( "(1,2)(-1,-6) and (2,-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237851 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the standard from of a parabola given by y = ax^2 + bx + c to write an<BR>\n" );
document.write( " equation of a parabola that passes through the given points, <BR>\n" );
document.write( "(1,2)(-1,-6) and (2,-3)<BR>\n" );
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document.write( "Write an equation for each pair<BR>\n" );
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document.write( "x=1; y=2<BR>\n" );
document.write( "a(1^2) + b(1) + c = 2<BR>\n" );
document.write( "a + b + c = 2<BR>\n" );
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document.write( "x=-1; y=-6<BR>\n" );
document.write( "a(-1^2) + b(-1) + c = -6<BR>\n" );
document.write( "a - b + c = -6<BR>\n" );
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document.write( "x=2; y=-3<BR>\n" );
document.write( "a(2^2) + b(2) + c = -3<BR>\n" );
document.write( "4a + 2b + c = -3<BR>\n" );
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document.write( "Subtract the 2nd equation from the 1st equation<BR>\n" );
document.write( "a + b + c = 2<BR>\n" );
document.write( "a - b + c = -6<BR>\n" );
document.write( "-----------------subtracting eliminates a & c, find b<BR>\n" );
document.write( "2b = 8<BR>\n" );
document.write( "b = 4<BR>\n" );
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document.write( "Replace b in the 1st equation<BR>\n" );
document.write( "a + 4 + c = 2<BR>\n" );
document.write( "a + c = 2 - 4<BR>\n" );
document.write( "a + c = -2<BR>\n" );
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document.write( "replace b in the 3rd equation<BR>\n" );
document.write( "4a + 2(4) + c = -3<BR>\n" );
document.write( "4a + c = -3 - 8<BR>\n" );
document.write( "4a + c = -11<BR>\n" );
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document.write( "Use elimination with these two equations<BR>\n" );
document.write( "4a + c = -11<BR>\n" );
document.write( "a + c = -2<BR>\n" );
document.write( "------------------subtraction eliminates c, find a<BR>\n" );
document.write( "3a = -9<BR>\n" );
document.write( "a = -3<BR>\n" );
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document.write( "Find c using the 1st equation<BR>\n" );
document.write( "-3 + 4 + c = 2<BR>\n" );
document.write( "1 + c = 2<BR>\n" );
document.write( "c = 2 - 1<BR>\n" );
document.write( "c = 1<BR>\n" );
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document.write( "The equation: y = -3x^2 + 4x + 1<BR>\n" );
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document.write( "check by replacing x and finding y for each given pair<BR>\n" );
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