document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46964>Question 46964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the function y  =  x2 - 6x + 8, perform the following tasks:<BR>\n" );
document.write( "a) 	Put the function in the form y = a(x - h)2 + k.<BR>\n" );
document.write( "Answer:  <BR>\n" );
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document.write( "b) 	What is the line of symmetry?<BR>\n" );
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document.write( "c) 	Graph the function using the equation in part a.  Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.<BR>\n" );
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document.write( "Explanation of graphing.  \r<BR>\n" );
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document.write( "d) 	In your own words, describe how this graph compares to the graph of y = x2?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31118 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=31118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Put the function in the form y = a(x - h)2 + k.<BR>\n" );
document.write( "y = x^2 - 6x + 8<BR>\n" );
document.write( "v(-b/2a,f(x))<BR>\n" );
document.write( "v(3,-1) so h = 3 and k = -1<BR>\n" );
document.write( "a = 1 while b = -6 and c = 8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+-+3%29%5E2+-+1 ALIGN=MIDDLE  ALT=\"y+=+%28x+-+3%29%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) What is the line of symmetry?<BR>\n" );
document.write( "Since the parabola is vertical, the line of symmetry is equal to the x-term in the vertex. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+-+3%29%5E2+-+1 ALIGN=MIDDLE  ALT=\"y+=+%28x+-+3%29%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "vertex(h,k)<BR>\n" );
document.write( "(distance from vertex to focus or from vertex to directrix = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4a ALIGN=MIDDLE  ALT=\"1%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Latus Rectum (distance touching the parabola going through the focus) = |1/a| = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28x+-+3%29%5E2+-+1%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28x+-+3%29%5E2+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d) In your own words, describe how this graph compares to the graph of y = x2?<BR>\n" );
document.write( "They are both parabolas. They both have the same value for 'a'. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a different vertex. The Latus Rectum and distances are the same. </SPAN>\n" );
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