document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139028>Question 139028</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131340212/algebrahomeworkh>Texas Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I was absent from school the day my class went over this and need help.  The question is:\r<BR>\n" );
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document.write( "Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each function.\r<BR>\n" );
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document.write( "Problem 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=2x%5E2%2B4 ALIGN=MIDDLE  ALT=\"+y=2x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101422 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not sure why you have the '=0' in there.  If it equals zero, then you only have two points -- no graph, no axis of symmetry, and no vertex.  Setting your expression equal to zero is how you discover where the graph crosses the x-axis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2B4 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "All parabolas can be expressed like this:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In your case, the values of a, b, and c are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=0+ ALIGN=MIDDLE  ALT=\"+b=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4 ALIGN=MIDDLE  ALT=\"c=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The x-coordinate of the vertex is found at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which also happens to be the equation of the axis of symmetry.  The y-coordinate of the vertex is just the value of the function at the value of the x-coordinate of the vertex, in other words:\r<BR>\n" );
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document.write( "<big><b>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28%28-b%29%2F2a%29 ALIGN=MIDDLE  ALT=\"f%28%28-b%29%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)</big></b>\r<BR>\n" );
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document.write( "So step 1 is to calculate the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the x-coordinate of the vertex.\r<BR>\n" );
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document.write( "Step 2: substitute that value for x in your original function and do the arithmetic.  The result is the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "Step 3: just write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substituting the value you calculated, to create the equation of the axis of symmetry. </SPAN>\n" );
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