document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55873>Question 55873</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" );
document.write( "Show work in this space.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) 	What is the equation for the line of symmetry for the graph of this function?<BR>\n" );
document.write( "Answer:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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( "Show graph here.   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation of graphing.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d) 	In your own words, describe how this graph compares to the graph of y = x2?<BR>\n" );
document.write( "Answer:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you tine  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37901 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=37901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi Tine,<BR>\n" );
document.write( "For the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E2+-+6x+%2B+8 ALIGN=MIDDLE  ALT=\"y++=++x%5E2+-+6x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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" );
document.write( "Show work in this space.  <BR>\n" );
document.write( "y=(x^2-6x+____)-___+8<BR>\n" );
document.write( "The blanks are fillied with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28b%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"c=%28b%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28%28-6%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"c=%28%28-6%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"c=%28-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c=9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2-6x%2B9%29-9%2B8 ALIGN=MIDDLE  ALT=\"y=%28x%5E2-6x%2B9%29-9%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor your perfect square trinomial.<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 equation for the line of symmetry for the graph of this function?<BR>\n" );
document.write( "Answer:  When the quadratic equation is in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the line of symmetry is x=h.  In this equation h=3, so the line of symmetry is x=3.\r<BR>\n" );
document.write( "\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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a+%28x+-+h%29%5E+2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a+%28x+-+h%29%5E+2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Show graph here.   <BR>\n" );
document.write( "1. The vertex is (h,k)=(3,-1)<BR>\n" );
document.write( "2. When a is positive the parabola opens up like a U, if it's negative, it opens down like an n.  a=+1, so ours opens up.<BR>\n" );
document.write( "3. If a>1, then it's skinnier (stretched vertically).  If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Ca%3C1 ALIGN=MIDDLE  ALT=\"-1%3Ca%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then it's wider (shrunk vertically).  a=1 in this case so it has a standard width.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation of graphing.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d) 	In your own words, describe how this graph compares to the graph of y = x2?<BR>\n" );
document.write( "Answer:  It is the same shape shifted horizontally h units (h=3, so 3 units to the right) and vertically k units (k=-1, so 1 unit down.)<BR>\n" );
document.write( "See for yourself:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-3%29%5E2-1%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!!  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );