document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91926>Question 91926</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073016023/algebrahomeworkh>Begining Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "Would you please help me with this problem:  <BR>\n" );
document.write( "Identify the axis of symetry, create a suitable table of values, and sketch th graph.  y=-x^2+6x-2\r<BR>\n" );
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document.write( "This is how far I have gotten, but I am not too sure if I have gotten this part right.<BR>\n" );
document.write( "y=-x^2+6x-2<BR>\n" );
document.write( "y+2=-x^2+6x<BR>\n" );
document.write( "y+2+9=x^2+6x+9<BR>\n" );
document.write( "y+11=(x+3)^2<BR>\n" );
document.write( "Can you please walk me through how to complete this type of problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66796 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=66796\">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%2B6x-2 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B6x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=-x%5E2%2B6x ALIGN=MIDDLE  ALT=\"y%2B2=-x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2++ ALIGN=MIDDLE  ALT=\"2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=-1%2A%28x%5E2-6%2Ax%29 ALIGN=MIDDLE  ALT=\"y%2B2=-1%2A%28x%5E2-6%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1++ ALIGN=MIDDLE  ALT=\"-1++\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This step is important since we want 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;\" > coefficient to be 1. This is where you made your mistake\r<BR>\n" );
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document.write( "Take half of the x coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2F2=-3 ALIGN=MIDDLE  ALT=\"-6%2F2=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2=9\"   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%2B2=-1%2A%28x%5E2-6%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"y%2B2=-1%2A%28x%5E2-6%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to the expression inside the parenthesis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2%2B%28-1%29%289%29=-1%2A%28x%5E2-6%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"y%2B2%2B%28-1%29%289%29=-1%2A%28x%5E2-6%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the parenthesis, we need to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%289%29 ALIGN=MIDDLE  ALT=\"%28-1%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the other side (remember, we factored out the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   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%2B2%2B%28-1%29%289%29=-1%2A%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B2%2B%28-1%29%289%29=-1%2A%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6%2Ax%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now the right side is a perfect square  (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2-9=-1%2A%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B2-9=-1%2A%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   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-7=-1%2A%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y-7=-1%2A%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2A%28x-3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"y=-1%2A%28x-3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7++ ALIGN=MIDDLE  ALT=\"7++\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y\r<BR>\n" );
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document.write( "Now the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2A%28x-3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"y=-1%2A%28x-3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in vertex 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;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=7 ALIGN=MIDDLE  ALT=\"k=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, for any quadratic in vertex 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;\" > the vertex is (h,k) and the axis of symmetry is x=h\r<BR>\n" );
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document.write( "So the vertex is  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the axis of symmetry is x=3\r<BR>\n" );
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document.write( "In order to create a table of suitable values, simply plug in x-values that are close to the axis of symmetry.\r<BR>\n" );
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document.write( "For instance, plug in x=1 (which is two units away from the axis of symmetry) to get y=3. So our first point is (1,3)\r<BR>\n" );
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document.write( "Now plug in x=2 (which is one unit away from the axis of symmetry) to get y=6. That makes our second point (2,6).\r<BR>\n" );
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document.write( "Since we know the vertex is (3,7), our third point is (3,7)\r<BR>\n" );
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document.write( "Since the graph is symmetric with respect to the axis of symmetry,  the x-value that is one unit to the right of the axis of symmetry (x=4) will have the same y-value as x=2 (since x=2 is also one unit away from the axis of symmetry). So our fourth point is (4,6)\r<BR>\n" );
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document.write( "Also the x-value that is two units to the right of the axis of symmetry (x=5) will have the same y-value as  x=1 (since x=1 is also two units away from the axis of symmetry). This makes our fifth point at (5,3)\r<BR>\n" );
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document.write( "So our table looks like\r<BR>\n" );
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document.write( "<TR><TD><TABLE frame=below><TR><TD> x</TD></TR></TABLE></TD><TD>|</TD><TD><TABLE frame=below><TR><TD> y</TD></TR></TABLE></TD></TR>\r\n" );
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document.write( "<TR><TD> 1</TD><TD>|</TD><TD> 3</TD></TR> \r\n" );
document.write( "<TR><TD> 2</TD><TD>|</TD><TD> 6</TD></TR> \r\n" );
document.write( "<TR><TD> 3</TD><TD>|</TD><TD> 7</TD></TR> \r\n" );
document.write( "<TR><TD> 4</TD><TD>|</TD><TD> 6</TD></TR> \r\n" );
document.write( "<TR><TD> 5</TD><TD>|</TD><TD> 3</TD></TR> \r\n" );
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document.write( "Now plot the points\r<BR>\n" );
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document.write( "Now connect the points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2B6x-2 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B6x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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