document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32365>Question 32365</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534419321/algebrahomeworkh>Elementary and Intermediate alegbra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the equation of the parabola that has an ordered pair (1,1), (0,2), and (3,5) as points on the graph.  I need to leave the answer in the form y= ax2 + bx +c.\r<BR>\n" );
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document.write( "Thanks\r<BR>\n" );
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document.write( "Sherri </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18924 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard equation of a parabola is y = ax^2+bx+c<BR>\n" );
document.write( "Substitute the ordered pairs in the above equation.<BR>\n" );
document.write( "For (1,1): 1 = a+b+c.........(1)<BR>\n" );
document.write( "For (0,2): 4 = c.............(2)<BR>\n" );
document.write( "For (3,5): 5 = 9a+3b+c......(3)<BR>\n" );
document.write( "From(2), we know c=4<BR>\n" );
document.write( "From (1) and (3):<BR>\n" );
document.write( "a+b = -3......(4)<BR>\n" );
document.write( "9a+3b=1......(5)<BR>\n" );
document.write( "Multiply (4) with -3:<BR>\n" );
document.write( "-3a-3b = 9<BR>\n" );
document.write( "9a+3b = 1<BR>\n" );
document.write( "Sum above two equations:<BR>\n" );
document.write( "6a = 10<BR>\n" );
document.write( "=>a=5/3<BR>\n" );
document.write( "Using equation (4): b=-3 - 5/3=-14/3<BR>\n" );
document.write( "The required equation is y = (5/3)x^2-(14/3)x+4 </SPAN>\n" );
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