document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830938>Question 830938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.\r<BR>\n" );
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document.write( "Vertex (-1,-6) point (5,18)\r<BR>\n" );
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document.write( "Please help very confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501016 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=501016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation for a quadratic function with vertex (h, k) can be written as f(x)=a(x-h)^2+k. <BR>\n" );
document.write( "The vertex of this function is (-1, -6), so once substituting that in, you have f(x)=a(x+1)^2 -6. <BR>\n" );
document.write( "and then there is the point (5, 18) that the function passes through, so substitute 5 for x and 18 for f(x). <BR>\n" );
document.write( "18 =a(5+1)^2 -6. <BR>\n" );
document.write( "now solve for a,<BR>\n" );
document.write( "18 =36a -6<BR>\n" );
document.write( "36a = 24<BR>\n" );
document.write( "a = 24/36 = 2/3<BR>\n" );
document.write( "so this quadratic function is f(x)=2/3(x+1)^2 -6.<BR>\n" );
document.write( "if you want it in the form f(x)=ax^2+bx+c, then multiply it out to get <BR>\n" );
document.write( "f(x) = 2x^2/3 +4x/3 -16/3\r<BR>\n" );
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