document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189058>Question 189058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to find the vertex but I don't really understand the steps to it. f(x)=x^2+10x+14<BR>\n" );
document.write( "do I have to do x^2 +10x+14-14?\r<BR>\n" );
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document.write( "the other one is f(x)=-x^2 +6x+20 to find the vertex and to determine if  there is a maximum or minimum value and what that value is... \r<BR>\n" );
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document.write( "the max.value would be k which would be 20 right? and minimum? \r<BR>\n" );
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document.write( "Anna </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141807 by </B><A HREF=/tutors/aboutme.mpl?userid=Tutor44><B>Tutor44(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Tutor44><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=141807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the vertex and examine if there is a maximum or minimum value you have to differentiate that function and put it equal to zero as following, I'll take the second problem in consideration, f(x) = - x^2 +6x +20\r<BR>\n" );
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document.write( "d/dx{f(x)} = d/dx(-x^2)+ d/dx (6x) + d/dx(20)<BR>\n" );
document.write( "=-2x + 6 + 0<BR>\n" );
document.write( "=-2x+6\r<BR>\n" );
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document.write( "now set, d/dx {f(x)} = 0<BR>\n" );
document.write( "or, -2x+6=0<BR>\n" );
document.write( "or, x= 3  put this in f(x), so y=f(3)=-3^2+6*3+20=29\r<BR>\n" );
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document.write( "so the vertex is (3,29)=(x,y)\r<BR>\n" );
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document.write( "Explanation: Differentiating with respect to (w.r.t) x means the rate of change of the value of the function w.r.t small change in value of x. so that point will be the highest (or lowest) where the change is zero. So we set it equal to zero.\r<BR>\n" );
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document.write( "Maximum or Minimum value: now at this point, the question is whether at this point the function has its highest value(maximum) or lowest value(minimum). If we again differentiate f(x) then if the differentiated value is positive (that means the value of the rate of change functions is increasing so it will be a minima) but if it is negative it means that the rate is decreasing indicating the value is maximum.\r<BR>\n" );
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document.write( "so d/dx^2 {f(x)}<BR>\n" );
document.write( "= d/dx {d/dx {f(x)}<BR>\n" );
document.write( "= d/dx (-2x) + d/dx(6) <BR>\n" );
document.write( "= -2+0 <BR>\n" );
document.write( "= -2\r<BR>\n" );
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document.write( "so that at this point the function has a maximum value\r<BR>\n" );
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document.write( "and the value is, f(3) = 29<BR>\n" );
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