document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549030>Question 549030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without graphing, find the vertex.<BR>\n" );
document.write( "f(x) = (x + 3)2 + 3\r<BR>\n" );
document.write( "\n" );
document.write( "Without graphing, find the vertex.<BR>\n" );
document.write( "f(x) = -(x + 1)2 + 1\r<BR>\n" );
document.write( "\n" );
document.write( "Without graphing, find the maximum value or minimum value.<BR>\n" );
document.write( "f(x) = (x + 3)2 – 4\r<BR>\n" );
document.write( "\n" );
document.write( "Without graphing, find the maximum value or minimum value.<BR>\n" );
document.write( "f(x) = (x - 1)2 + 1\r<BR>\n" );
document.write( "\n" );
document.write( "Determine whether there is a maximum or minimum value for the given function, and find that value.\r<BR>\n" );
document.write( "\n" );
document.write( "f(x) = -x2 - 18x – 83\r<BR>\n" );
document.write( "\n" );
document.write( "I don't quite understand on how to find the vertex of one line, finding maximum/minimum value. <BR>\n" );
document.write( "Any help is GREATLY appreciated! Merry Christmas! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357449 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex of a parabola is the point where the derivative is equal to 0.<BR>\n" );
document.write( "a) f(x) = (x+3)^2 + 3<BR>\n" );
document.write( "df/dx = 0 = 2(x+3)(1) -> x = -3<BR>\n" );
document.write( "f(-3) = (0)^2 + 3 = 3<BR>\n" );
document.write( "So the vertex is (-3,3)<BR>\n" );
document.write( "The other vertices are found in a similar fashion<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f(x) = (x+3)^2 - 4<BR>\n" );
document.write( "Since this parabola opens upward, it will have a minimum. <BR>\n" );
document.write( "The minimum will be obtained when the 1st term=0: (x+3)^2 = 0 -> x = -3<BR>\n" );
document.write( "So the minimum value is -4<BR>\n" );
document.write( "f(x) = -x^2 - 18x - 83<BR>\n" );
document.write( "Take the derivative and set=0:<BR>\n" );
document.write( "df/dx = 0 = -2x - 18 -> x = -9<BR>\n" );
document.write( "f(-9) = -(-9)^2 - 18(-9) - 83 = -2<BR>\n" );
document.write( "This will be a maximum since the parabola opens downward<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );