document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=701259>Question 701259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial of degree &#8804;2 [of the form f (t) = a + bt + ct^2] whose graph goes through the points (1, p), (2, q), (3,r), where p, q, r are arbitrary constants. Does such a polynomial exist for all values of p, q, r? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432318 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=432318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial of degree &#8804;2 [of the form f (t) = a + bt + ct^2] whose graph goes through the points (1, p), (2, q), (3,r), where p, q, r are arbitrary constants. Does such a polynomial exist for all values of p, q, r?<BR>\n" );
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document.write( "Form: ax^2 + bx + c = y<BR>\n" );
document.write( "Using (1,p) you get: a + b + c = p<BR>\n" );
document.write( "Using (2,q) you get: 4a+2b + c = q<BR>\n" );
document.write( "Using (3,r) you get: 9a+3b + c == r\r<BR>\n" );
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document.write( "Solutions exist as long as the coefficient<BR>\n" );
document.write( "matrix is not singular i.e, as long as the<BR>\n" );
document.write( "determinant of that matrix is not zero.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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