document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79162>Question 79162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this problem?  I'm stuck!!! I'm in a class that is over my head.  Help!!!!!!!!!!!!!!!!!!!!\r<BR>\n" );
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document.write( "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" );
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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" );
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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" );
document.write( "Answer:  \r<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 #56824 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=56824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Put the function<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2-6x%2B8 ALIGN=MIDDLE  ALT=\"y+=+x%5E2-6x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the form <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;\" ><BR>\n" );
document.write( "To do this you will start with the given function and you will \"complete the square\".\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%2B8 ALIGN=MIDDLE  ALT=\"y+=+x%5E2-6x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract the constant (8) from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8+=+x%5E2-6x ALIGN=MIDDLE  ALT=\"y-8+=+x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now complete the square in the x-terms by adding the square of half the x-coefficient (that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%2F2%29%5E2+=+9 ALIGN=MIDDLE  ALT=\"%28-6%2F2%29%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1+=+x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"y%2B1+=+x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1+=+%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B1+=+%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract 1 from both sides.<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;\" > Compare this with:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "h = 3<BR>\n" );
document.write( "k = -1\r<BR>\n" );
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document.write( "b) The equation of the line of symmetry is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+h ALIGN=MIDDLE  ALT=\"x+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so in this case, since h = 3, the equation of the line of symmetry is:<BR>\n" );
document.write( "<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;\" > This is a vertical line passing through the point (3, 0)\r<BR>\n" );
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document.write( "c) It is not necessary to plot points to graph the function in this form because:<BR>\n" );
document.write( "1) You know the equation of the line of symmetry.<BR>\n" );
document.write( "2) You know that the parabola opens upward because a>0 (a is positive).<BR>\n" );
document.write( "3) You know (or can find) the location of the vertex of the parabola.  Thi is given by (h, k) or (3, -1)<BR>\n" );
document.write( "4) You can find the x- and y-intercepts of the function by:<BR>\n" );
document.write( "x-intercepts: Set y = 0 and solve for x.<BR>\n" );
document.write( "<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;\" > Add 1 to both sides.<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;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29%5E2+=+sqrt%281%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29%5E2+=+sqrt%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+1 ALIGN=MIDDLE  ALT=\"x-3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > + or - Add 3 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2B1 ALIGN=MIDDLE  ALT=\"x+=+3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3-1 ALIGN=MIDDLE  ALT=\"x+=+3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > These are the x-intercepts.<BR>\n" );
document.write( "y-intercept: Set x = 0 and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280-3%29%5E2+-1 ALIGN=MIDDLE  ALT=\"y+=+%280-3%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=y+=+9-1 ALIGN=MIDDLE  ALT=\"y+=+9-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8 ALIGN=MIDDLE  ALT=\"y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > This the y-intecept.\r<BR>\n" );
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document.write( "Here is the graph (in red): I'll add the graph of the function <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 green) so you can compare the two.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C6%2C-4%2C10%2C%28x-3%29%5E2-1%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C6%2C-4%2C10%2C%28x-3%29%5E2-1%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d) I'll leave the explanation to you.  Look at the two graphs and try to see what effects the values of h and k have on the placement of the second (green) graph compared to the first (red) graph.<BR>\n" );
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