document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190090>Question 190090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the quadratic function with vertex (6, -40) and passing through the point (3,50) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142664 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=142664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the quadratic function with vertex (6, -40) and passing through the point (3,50)<BR>\n" );
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document.write( "The vertex occurs when x = -b/2a = 6<BR>\n" );
document.write( "So 12a = -b<BR>\n" );
document.write( "b = -12a<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "General form of quadratic:<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "y = ax^2 -12ax + c<BR>\n" );
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document.write( "Since the function passes thru (3,50), substitute to solve for \"c\".<BR>\n" );
document.write( "50 = a(9) -12a(3) + c<BR>\n" );
document.write( "50 = -27a + c<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Since the function passes thru (6.-40)<BR>\n" );
document.write( "-40 = a(36) -12a(6) + c<BR>\n" );
document.write( "-40 = -36a + c<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Solve 2-equation system by substitution:<BR>\n" );
document.write( "c = 27a+50<BR>\n" );
document.write( "c = 36a-40<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "27a+50 = 36a-40<BR>\n" );
document.write( "9a = 90<BR>\n" );
document.write( "a = 10<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Solve for \"c\":<BR>\n" );
document.write( "c = 36(10)-40 = 320\r<BR>\n" );
document.write( "\n" );
document.write( "===============================<BR>\n" );
document.write( "Since b = -12a, b = -120<BR>\n" );
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document.write( "Equation: y = 10x^2 -120x + 320<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );