document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110039>Question 110039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the axis of symmetry.\r<BR>\n" );
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document.write( "y=x^2-10x+7\r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80189 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a quadratic equation of the standard form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the axis of symmetry will be given by the equation:<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;\" ><BR>\n" );
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document.write( "Note that this equation for the axis of symmetry is the first term of the solution for x that is<BR>\n" );
document.write( "provided by the quadratic formula:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this problem you are given the quadratic equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-10x%2B7 ALIGN=MIDDLE  ALT=\"y=x%5E2-10x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can convert this to the standard quadratic form by setting y equal to zero to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-10x%2B7 ALIGN=MIDDLE  ALT=\"0=x%5E2-10x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and then transposing the equation (reversing sides) to change it to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2B7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2B7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By comparing this equation, term by term, with the standard form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that \"a\" [the multiplier of 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;\" >] must be 1, \"b\" [the multiplier<BR>\n" );
document.write( "of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ] must be -10, and \"c\" [the constant] must be +7.<BR>\n" );
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document.write( "Now that the values of a, b, and c have been found by comparing the standard form of<BR>\n" );
document.write( "the quadratic equation to the form given in the problem, the line of symmetry can be<BR>\n" );
document.write( "found by substituting these values into the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"a\" was found to be 1 and \"b\" was found to be -10. Substituting these values results<BR>\n" );
document.write( "in the line of symmetry equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28-10%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+-%28-10%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2F2+=+5 ALIGN=MIDDLE  ALT=\"x+=+10%2F2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the equation for the line of symmetry is, therefore, x = +5 and the graph of this line is <BR>\n" );
document.write( "a vertical line through the point +5 on the x-axis because the equation tells you that<BR>\n" );
document.write( "no matter what the value of y, x is always +5.  So all the following points are on the line:<BR>\n" );
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document.write( "(5, 10) (5, 5) (5, 0) (5, -5) (5, -10) and so on<BR>\n" );
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document.write( "If you plot all of these points on a graph you will see that they lie on the vertical<BR>\n" );
document.write( "line through +5 on the x-axis.<BR>\n" );
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document.write( "I hope this helps you to see how to work this problem.<BR>\n" );
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