document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138>Question 1138</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi can someone help me with determining the equation of the quadratic function <BR>\n" );
document.write( "with a vertex of (3,5) and point (5,1)\r<BR>\n" );
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document.write( "and a parabola with the points (-1,4), (1, -2) and (2,1)  \r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Since the quadratic equation with vertex (a,b) should be as:<BR>\n" );
document.write( "  y - b = c (x-a)^2,<BR>\n" );
document.write( " Now (a,b) = (3,5) and (5,1)is on the graph, we have<BR>\n" );
document.write( " 1 - 5 = c (5 -3)^2 = 4 c <BR>\n" );
document.write( " and so c = -1, the quadratic equation as<BR>\n" );
document.write( "  y - 5 = - (x - 3)^2\r<BR>\n" );
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document.write( " Next, let the equation of the parabola be y = a x^2 + bx + c<BR>\n" );
document.write( " Since it passing through (-1,4), (1, -2) and (2,1).<BR>\n" );
document.write( " We have<BR>\n" );
document.write( "   a - b + c = 4 ...(1)<BR>\n" );
document.write( "   a + b + c = -2 ...(2)<BR>\n" );
document.write( "  4a + 2b + c = 1 ...(3)\r<BR>\n" );
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document.write( "  By (2)-(1), we have 2b = -6, so b=-3.<BR>\n" );
document.write( "  Replace b by -3 in (1),we have a + c = 1...(4)<BR>\n" );
document.write( "  Replace b by -3 in (3),we have 4a + c = 7...(5)<BR>\n" );
document.write( "  By (5)-(4), we have 3a=6, a =2.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Replace a by 2 in (4),we have c= 1-2 = -1.\r<BR>\n" );
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document.write( "  Hence,the equation of the parabola be y = 2 x^2 - 3x -1.\r<BR>\n" );
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document.write( "   *   <BR>\n" );
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