document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144744>Question 144744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having some trouble graphing this eqaution: y=x^2-2x-8<BR>\n" );
document.write( "The question asks that I find the y and x intercepts and the vertex. I got the x intercepts at 4 and-2, the y intercept at 0,-8 and the vertex at -1,-7. The vertex doesnt seem to work though. I'd appreciate any help I could get.<BR>\n" );
document.write( "~Kyle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105472 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=105472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Everything is correct except for the vertex\r<BR>\n" );
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document.write( "To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)\r<BR>\n" );
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document.write( "To find the axis of symmetry, use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"y=x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=1 and b=-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28--2%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28--2%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=-2 and a=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=2%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -2 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%29%2F2 ALIGN=MIDDLE  ALT=\"x=%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the axis of symmetry is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Lets plug this into the equation to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29 ALIGN=MIDDLE  ALT=\"f%281%29\"   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=f%28x%29=x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=%281%29%5E2-2%281%29-8 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29%5E2-2%281%29-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=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=f%281%29=%281%29-2%281%29-8 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29-2%281%29-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 1 to the second power to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-9 ALIGN=MIDDLE  ALT=\"f%281%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (1,-9)\r<BR>\n" );
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document.write( "So let's use the this  (along with the other pieces you solved for) to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"y=x%5E2-2x-8\"   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=drawing%28500%2C500%2C-9%2C11%2C-12%2C5%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28500%2C500%2C-9%2C11%2C-12%2C5%2C+x%5E2-2x-8%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"y=x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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