document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159196>Question 159196</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321466071/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find b such that f(x)=-2x^2+bx-30 has a maximum value of 2 and the vertex is located in the second quadrant. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117333 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=117333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find b such that f(x)=-2x^2+bx-30 has a maximum value of 2 and the vertex is located in the second quadrant.<BR>\n" );
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document.write( "You have a quadratic equation with a = -2, b = b, and c = -30<BR>\n" );
document.write( "Maximum value for f(x) occurs when x = -b/2a = -b/(-4) = b/4<BR>\n" );
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document.write( "Then f(b/4) = -2(b/4)^2 + b(b/4) -30 = 2\r<BR>\n" );
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document.write( "-b^2/8 + b^2/4 - 30 = 2<BR>\n" );
document.write( "b^2 - 2b^2 + 240 = -16<BR>\n" );
document.write( "b^2 = 256<BR>\n" );
document.write( "b = +16 or b = -16<BR>\n" );
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document.write( "If b = 16 the vertex is at x= b/4 = 16 and x = 64 which is in the 1st quadrant<BR>\n" );
document.write( "If b = -16 the vertex is at x=b/4 = -16 and x = -64 which is in the 2nd Quad.<BR>\n" );
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document.write( "Answer b = -16<BR>\n" );
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document.write( "f(x)=-2x^2-16x-30<BR>\n" );
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document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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