document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103996>Question 103996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
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document.write( "I need help finding the equation of the axis of symmetry and the coordinates of the vertex of the graph of: y=2x^2+4x-5\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75668 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=75668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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=2x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=2 and b=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x=%28-4%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=4 and a=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%29%2F4 ALIGN=MIDDLE  ALT=\"x=%28-4%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\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%28-1%29 ALIGN=MIDDLE  ALT=\"f%28-1%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=2x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2%2B4x-5\"   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%28-1%29=2%28-1%29%5E2%2B4%28-1%29-5 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%28-1%29%5E2%2B4%28-1%29-5\"   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%28-1%29=2%281%29%2B4%28-1%29-5 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%281%29%2B4%28-1%29-5\"   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%28-1%29=2%2B4%28-1%29-5 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%2B4%28-1%29-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by 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=f%28-1%29=2%2B-4-5 ALIGN=MIDDLE  ALT=\"f%28-1%29=2%2B-4-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4 by -1 to get -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-7 ALIGN=MIDDLE  ALT=\"f%28-1%29=-7\"   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,-7)\r<BR>\n" );
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document.write( "Notice if you graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28900%2C900%2C-11%2C9%2C-17%2C3%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28900%2C900%2C-11%2C9%2C-17%2C3%2C+2x%5E2%2B4x-5%29%2C%0D%0Acircle%28-3%2C1%2C0.05%29%2C%0D%0Acircle%28-3%2C1%2C0.08%29%2C%0D%0Acircle%28-2%2C-5%2C0.05%29%2C%0D%0Acircle%28-2%2C-5%2C0.08%29%2C%0D%0Acircle%28-1%2C-7%2C0.05%29%2C%0D%0Acircle%28-1%2C-7%2C0.08%29%2C%0D%0Acircle%280%2C-5%2C0.05%29%2C%0D%0Acircle%280%2C-5%2C0.08%29%2C%0D%0Acircle%281%2C1%2C0.05%29%2C%0D%0Acircle%281%2C1%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and you can see that the vertex is (-1,-7)\r<BR>\n" );
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