document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=489817>Question 489817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x) = 3x^2 - 30x - 1<BR>\n" );
document.write( "a. determine without graphing, does the function have a minimum or maximum value?<BR>\n" );
document.write( "b.  Find the minimum or maximum value and determine where it occurs.<BR>\n" );
document.write( "c.  Identify the functions domain and range </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334111 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=334111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x) = 3x^2 - 30x - 1<BR>\n" );
document.write( "a. determine without graphing, does the function have a minimum or maximum value?<BR>\n" );
document.write( "b. Find the minimum or maximum value and determine where it occurs.<BR>\n" );
document.write( "c. Identify the functions domain and range<BR>\n" );
document.write( "**<BR>\n" );
document.write( "y=3x^2-30x-1<BR>\n" );
document.write( "a. Because the lead coefficient is >0, this parabola opens upwards which means function has a minimum.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b.completing the square<BR>\n" );
document.write( "y=3(x^2-10x+25)-1-75<BR>\n" );
document.write( "y=3(x-5)^2-76<BR>\n" );
document.write( "This is an equation of a parabola of the standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "coordinates of the vertex:(5,-76)<BR>\n" );
document.write( "minimum value=-76 at x=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c. Domain (-&#8734;,&#8734;), Range [-76,&#8734;) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );