document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31878>Question 31878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the function y=x2-4x-5, perform the following tasks:<BR>\n" );
document.write( "a) Put the function in the form y=a(x-h)2 +k ....the 2 after x is x squared, and the 2 after h is (x-h)squared<BR>\n" );
document.write( "b)what is the line of symmetry?<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   (the 2 after (x-h) is squared<BR>\n" );
document.write( "d) how does this graph compare to the graph of y=x2(xsquared) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18479 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=18479\">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%5E2-4x-5+ ALIGN=MIDDLE  ALT=\"+y=x%5E2-4x-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2a=-4<BR>\n" );
document.write( "--> a = -2<BR>\n" );
document.write( "and so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+4 ALIGN=MIDDLE  ALT=\"a%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2-4x%28%2B4-4%29-5+ ALIGN=MIDDLE  ALT=\"+y=x%5E2-4x%28%2B4-4%29-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> the +4-4 is zero, so we haven't actually altered the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=%28x%5E2-4x%2B4%29-4-5+ ALIGN=MIDDLE  ALT=\"+y=%28x%5E2-4x%2B4%29-4-5+\"   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-2%29%5E2-4-5+ ALIGN=MIDDLE  ALT=\"+y=%28x-2%29%5E2-4-5+\"   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-2%29%5E2-9+ ALIGN=MIDDLE  ALT=\"+y=%28x-2%29%5E2-9+\"   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-2%29%5E2%2B%28-9%29+ ALIGN=MIDDLE  ALT=\"+y=%28x-2%29%5E2%2B%28-9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is now of the form required.\r<BR>\n" );
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document.write( "b. Line of symmetry is x=2\r<BR>\n" );
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document.write( "c. We know the apex of the curve...it is (2,-9) and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is positive, meaning it is u-shaped rather than n-shaped. So we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-4%2C8%2C-10%2C4%2Cx%5E2-4x-5%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-4%2C8%2C-10%2C4%2Cx%5E2-4x-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, purely looking at the equation in this form does not \"instantly\" tell us the intercepts on the axes... some algebra, minimal yes, is still required.\r<BR>\n" );
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document.write( "d. <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;\" > moved by 2 units to the right gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then this moved by 9 units down is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-2%29%5E2+-+9 ALIGN=MIDDLE  ALT=\"y=%28x-2%29%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here are all 3 stages: <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-2%29%5E2-9 ALIGN=MIDDLE  ALT=\"y=%28x-2%29%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the same scales, so you can see them:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2Cx%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2Cx%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2C%28x-2%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2C%28x-2%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2C%28x-2%29%5E2-9%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-4%2C8%2C-10%2C20%2C%28x-2%29%5E2-9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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