document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28424>Question 28424</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 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 #15449 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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;\" > needs to be converted to a version that has duplicate factors. It is called \"completing the square\". To do this, we will look at just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E2+-+6x ALIGN=MIDDLE  ALT=\"y++=++x%5E2+-+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and see what third number we need to add to it.\r<BR>\n" );
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document.write( "If i added +9 to the above equation, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E2+-+6x+%2B+9 ALIGN=MIDDLE  ALT=\"y++=++x%5E2+-+6x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then this can be factorised as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is the form i want. So...\r<BR>\n" );
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document.write( "<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;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8 ALIGN=MIDDLE  ALT=\"y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Can you see that i have added in a \"+9\" and a \"-9\", so overall, the equation is unchanged...i am just messing it around a bit.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8 ALIGN=MIDDLE  ALT=\"y++=++x%5E2+-+6x++%2B+9+-+9+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++%28x-3%29%5E2+-+9+%2B+8 ALIGN=MIDDLE  ALT=\"y++=++%28x-3%29%5E2+-+9+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and finally<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;\" > which is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++%28x-3%29%5E2+%2B+%28-1%29 ALIGN=MIDDLE  ALT=\"y++=++%28x-3%29%5E2+%2B+%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is the form the Q wanted. As to why? well, in this form, the 3 and the -1 tell us the position of the turning point in the quadratic..the point where the curve turns... it is at (3,-1)\r<BR>\n" );
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document.write( "so the line of symmetry is x=3\r<BR>\n" );
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document.write( "No need to plot the graph, we can sketch it... we know the turning point. Only other things to know are where does the curve cross the x- and y-axes?\r<BR>\n" );
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document.write( "Crossing the y-axis is when x=0<BR>\n" );
document.write( "<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;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=++%280%29%5E2+-+6%280%29+%2B+8 ALIGN=MIDDLE  ALT=\"y++=++%280%29%5E2+-+6%280%29+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> y = 8\r<BR>\n" );
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document.write( "Crossing the x-axis is when y=0<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;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0++=++%28x-3%29%5E2+-+1 ALIGN=MIDDLE  ALT=\"0++=++%28x-3%29%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+-+1+=+0 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29+=+sqrt%281%29+ ALIGN=MIDDLE  ALT=\"%28x-3%29+=+sqrt%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29+=+-sqrt%281%29+ ALIGN=MIDDLE  ALT=\"%28x-3%29+=+-sqrt%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x-3 = 1 OR x-3 = -1<BR>\n" );
document.write( "--> x = 4 OR x = 2\r<BR>\n" );
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document.write( "Graph is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C6%2C-5%2C10%2Cx%5E2+-+6x+%2B+8%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C6%2C-5%2C10%2Cx%5E2+-+6x+%2B+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Compares to <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;\" > in the fact that it is the same curve just moved... how many units to the right? How many units down? You say.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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