document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472862>Question 472862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to find the x and y intercepts axis of symmentary and vertex of this equation<BR>\n" );
document.write( "y= -x^2/2+3x+8\r<BR>\n" );
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document.write( "to find x intercepts told to mutiply by -2, which makes equation<BR>\n" );
document.write( "y=x^-6x-16<BR>\n" );
document.write( "would I find axis of symmentry and vertex from the new values or from original equation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324206 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, make the equation = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=+-x%5E2%2F2%2B3x%2B8 ALIGN=MIDDLE  ALT=\"y=+-x%5E2%2F2%2B3x%2B8\"   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=0=+-x%5E2%2F2%2B3x%2B8 ALIGN=MIDDLE  ALT=\"0=+-x%5E2%2F2%2B3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >......... multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   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=0=+x%5E2-6x-8 ALIGN=MIDDLE  ALT=\"0=+x%5E2-6x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x-8=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........use quadratic formula\r<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;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%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=x+=+%286+%2B-+sqrt%2836%2B32+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%2836%2B32+%29%29%2F2+\"   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=x+=+%286+%2B-+sqrt%2868%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%2868%29%29%2F2+\"   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=x+=+%286+%2B-+8.25%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+8.25%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B8.25%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B8.25%29%2F2+\"   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=x+=+14.25%2F2+ ALIGN=MIDDLE  ALT=\"x+=+14.25%2F2+\"   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=x+=+7.125+ ALIGN=MIDDLE  ALT=\"x+=+7.125+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+-8.25%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%286+-8.25%29%2F2+\"   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=x+=+-2.25%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-2.25%2F2+\"   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=x+=-1.125+ ALIGN=MIDDLE  ALT=\"x+=-1.125+\"   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-intercept ALIGN=MIDDLE  ALT=\"y-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the equation, and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=+-0%5E2%2F2%2B3%2A0%2B8 ALIGN=MIDDLE  ALT=\"y=+-0%5E2%2F2%2B3%2A0%2B8\"   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=+0%2B0%2B8 ALIGN=MIDDLE  ALT=\"y=+0%2B0%2B8\"   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=+8 ALIGN=MIDDLE  ALT=\"y=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > are at points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.125 ALIGN=MIDDLE  ALT=\"7.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.125 ALIGN=MIDDLE  ALT=\"-1.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept ALIGN=MIDDLE  ALT=\"y-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Axis of symmetry can be found using the formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"a=%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   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=x+=+-b%2F2a=-3%2F2%28-1%2F2%29=-3%2Fcross%282%29%28-1%2Fcross%282%29%29=-3%2F-1=3 ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a=-3%2F2%28-1%2F2%29=-3%2Fcross%282%29%28-1%2Fcross%282%29%29=-3%2F-1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Vertex is the x/y values for the max or min and occurs at the axis of symmetry; so Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > value: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-3%5E2%2F2%2B3%2A3%2B8 ALIGN=MIDDLE  ALT=\"y=+-3%5E2%2F2%2B3%2A3%2B8\"   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=+-9%2F2%2B9%2B8 ALIGN=MIDDLE  ALT=\"y=+-9%2F2%2B9%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-4.5%2B17 ALIGN=MIDDLE  ALT=\"y=+-4.5%2B17\"   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=12.5 ALIGN=MIDDLE  ALT=\"y=12.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the Vertex is at (<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=12.5 ALIGN=MIDDLE  ALT=\"12.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "now see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C10%2C+-10%2C+20%2C-x%5E2%2F2%2B3x%2B8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C10%2C+-10%2C+20%2C-x%5E2%2F2%2B3x%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );