document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199166>Question 1199166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the cordinate of the vertex of the graph of f(x)  f(x)=x2-4x+ 13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832874 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "f(x) = x^2-4x+13<BR>\n" );
document.write( "is the given equation\r<BR>\n" );
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document.write( "Think of it as <BR>\n" );
document.write( "y = x^2-4x+13\r<BR>\n" );
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document.write( "Compare it to<BR>\n" );
document.write( "y = ax^2+bx+c\r<BR>\n" );
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document.write( "We have the following coefficients<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = 13\r<BR>\n" );
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document.write( "The vertex is located at (h,k).<BR>\n" );
document.write( "Let's compute the x coordinate of the vertex.<BR>\n" );
document.write( "h = -b/(2a)<BR>\n" );
document.write( "h = -(-4)/(2*1)<BR>\n" );
document.write( "h = 2\r<BR>\n" );
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document.write( "Then plug this into the original equation to find the y coordinate of the vertex.<BR>\n" );
document.write( "y = x^2-4x+13<BR>\n" );
document.write( "y = 2^2-4*2+13<BR>\n" );
document.write( "y = 4-8+13<BR>\n" );
document.write( "y = -4+13<BR>\n" );
document.write( "y = 9<BR>\n" );
document.write( "This is the value of k in (h,k)\r<BR>\n" );
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document.write( "Since<BR>\n" );
document.write( "h = 2<BR>\n" );
document.write( "k = 9<BR>\n" );
document.write( "We can then say the vertex is located at (h,k) = (2,9)<BR>\n" );
document.write( "This is the lowest point on the parabola since a = 2 is positive, causing the parabola to open upward.\r<BR>\n" );
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document.write( "The vertex form would be: <BR>\n" );
document.write( "y = a(x-h)^2+k<BR>\n" );
document.write( "y = 1(x-2)^2+9<BR>\n" );
document.write( "y = (x-2)^2+9<BR>\n" );
document.write( "I'll let the student expand that vertex form out so you get the original equation again. <BR>\n" );
document.write( "This helps confirm the correct vertex form.\r<BR>\n" );
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document.write( "Answer: The vertex is located at (2,9)<BR>\n" );
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