document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115728>Question 115728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I Need to Find The Range Of The Given Function.<BR>\n" );
document.write( "f(x)=-4x^2-24x-41<BR>\n" );
document.write( "I graphed it on my calculator but i don't know how to find my range or y-values help me please thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84204 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=84204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I Need to Find The Range Of The Given Function.<BR>\n" );
document.write( "f(x)=-4x^2-24x-41<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The graph would be a parabola with a maximum point.<BR>\n" );
document.write( "That maximum occurs when x=-b/2a = 24/-8 = -3<BR>\n" );
document.write( "f(-3) = -4(-3)^2 -24(-3)-41<BR>\n" );
document.write( "f(-3) = -36 + 72-41<BR>\n" );
document.write( "f(-3) = 36-41<BR>\n" );
document.write( "f(-3) = -5<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "So the highest y-value is -5.<BR>\n" );
document.write( "Therefore the range is : all Real numbers <= -5<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-50%2C20%2C-4x%5E2-24x-41%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-50%2C20%2C-4x%5E2-24x-41%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );