document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622054>Question 622054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine where the function is increasing and where it is decreasing.\r<BR>\n" );
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document.write( "f(x)=-x^2-4x+5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391098 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine where the function is increasing and where it is decreasing.\r<BR>\n" );
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document.write( "f(x)=-x^2-4x+5<BR>\n" );
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document.write( "Because it is a polynomial of degree 2, we know it is a parabola.<BR>\n" );
document.write( "And, because the coefficient associated with the x^2 term is negative, we know it opens downwards.  So, the max will be at the vertex.<BR>\n" );
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document.write( "Axis of symmetry:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -(-4)/(2(-1))<BR>\n" );
document.write( "x = 4/(-2)<BR>\n" );
document.write( "x = -2<BR>\n" );
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document.write( "function is increasing in the range of:<BR>\n" );
document.write( "(-oo, -2)<BR>\n" );
document.write( "function is decreasing in the range of:<BR>\n" );
document.write( "(-2, +oo)<BR>\n" );
document.write( "where oo indicates infinity </SPAN>\n" );
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