document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=674561>Question 674561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help please, \r<BR>\n" );
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document.write( "Find the equation of the quadratic function <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;\" > whose graph runs through points (3,2),(4,3),(5,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419363 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=419363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the quadratic function y = ax^2 + bx+ c, whose graph runs through points (3,2),(4,3),(5,2)<BR>\n" );
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document.write( "Write a equation for each x,y pair, replacing x and y<BR>\n" );
document.write( "3,2: 9a + 3b + c = 2<BR>\n" );
document.write( "4,3: 16a + 4b + c = 3<BR>\n" );
document.write( "5,2: 25a + 5b + c = 2<BR>\n" );
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document.write( "Use elimination and substitution<BR>\n" );
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document.write( "Subtract the 1st equation from the 2nd<BR>\n" );
document.write( "16a + 4b + c = 3<BR>\n" );
document.write( " 9a + 3b + c = 2<BR>\n" );
document.write( "-----------------Subtraction eliminates c<BR>\n" );
document.write( "7a + b = 1<BR>\n" );
document.write( "b = (1-7a), for substitution<BR>\n" );
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document.write( "Subtract the 1st equation from the 3rd<BR>\n" );
document.write( "25a + 5b + c = 2<BR>\n" );
document.write( " 9a + 3b + c = 2<BR>\n" );
document.write( "-----------------Subtraction eliminates c<BR>\n" );
document.write( "16a + 2b = 0<BR>\n" );
document.write( "Replace b with (1-7a)<BR>\n" );
document.write( "16a + 2(1-7a) = 0<BR>\n" );
document.write( "16a + 2 - 14a = 0<BR>\n" );
document.write( "2a = -2<BR>\n" );
document.write( "a = -1<BR>\n" );
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document.write( "Find b<BR>\n" );
document.write( "b = 1 - 7(-1)<BR>\n" );
document.write( "b = 1 + 7<BR>\n" );
document.write( "b = 8<BR>\n" );
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document.write( "Find c using the 1st original equation<BR>\n" );
document.write( "9(-1) + 3(8) + c = 2<BR>\n" );
document.write( "-9 + 24 + c = 2<BR>\n" );
document.write( "15 + c = 2<BR>\n" );
document.write( "c = 2 - 15<BR>\n" );
document.write( "c = -13<BR>\n" );
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document.write( "The equation, y = -x^2 + 8x - 13<BR>\n" );
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document.write( "YOu can confirm this, substitute for x and find y, for each given pair </SPAN>\n" );
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