document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=377876>Question 377876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me. I need to find write the quadratic function for a given set of points (0,-4)(1,0)(2,2). I keep getting different answers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268504 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=268504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  then using the coordinates of the points, <BR>\n" );
document.write( "-4 = c,<BR>\n" );
document.write( "0 = a+b+c,<BR>\n" );
document.write( "2 = 4a + 2b + c.\r<BR>\n" );
document.write( "\n" );
document.write( "substituting the first equation into the 2nd, we get a+b = 4.<BR>\n" );
document.write( "substituting the first equation into the 3rd, we get 4a+2b = 6, or 2a+b = 3.\r<BR>\n" );
document.write( "\n" );
document.write( "So b = 4-a.  Putting this into 2a+b = 3, we get<BR>\n" );
document.write( "2a + 4-a = 3, or a = -1.  This would give b = 4--1 = 5.<BR>\n" );
document.write( "Thus the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2+%2B+5x+-+4 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2+%2B+5x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );