document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=753661>Question 753661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the equation y=x^2 + 16x + 8 <BR>\n" );
document.write( "I have to find the vertex and x intercept of this equation.  I am using <BR>\n" );
document.write( "x = -b/2a.  In trying to complete the square my answers are x= -.5 and x= -15,5. Thus I have the x intercepts as (-.5,0) and (-15.5,0).  I don't think those answers are right and I am confused about how to find the vertex. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458504 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=458504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex form of a parabola's equation is generally expressed as :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+a%28x-h%29%5E2%2Bk+ ALIGN=MIDDLE  ALT=\"y=+a%28x-h%29%5E2%2Bk+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the vertex\r<BR>\n" );
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document.write( "write your equation in vertex form \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2+%2B+16x+%2B+8 ALIGN=MIDDLE  ALT=\"y=x%5E2+%2B+16x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >..complete the square \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2+%2B+16x%2B__%29+%2B+8 ALIGN=MIDDLE  ALT=\"y=%28x%5E2+%2B+16x%2B__%29+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2=64 ALIGN=MIDDLE  ALT=\"8%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A8=16 ALIGN=MIDDLE  ALT=\"2%2A8=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   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=%28x%5E2+%2B+16x%2B64%29-64+%2B+8 ALIGN=MIDDLE  ALT=\"y=%28x%5E2+%2B+16x%2B64%29-64+%2B+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=y=%28x+%2B+8%29%5E2-56 ALIGN=MIDDLE  ALT=\"y=%28x+%2B+8%29%5E2-56\"   DISABLED_style= \"max-width:90%; height:auto;\" >...as you can see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-8 ALIGN=MIDDLE  ALT=\"h=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-56 ALIGN=MIDDLE  ALT=\"k=-56\"   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=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-56 ALIGN=MIDDLE  ALT=\"-56\"   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-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" >: to find them, set <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;\" > 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=0=%28x+%2B+8%29%5E2-56 ALIGN=MIDDLE  ALT=\"0=%28x+%2B+8%29%5E2-56\"   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=56=%28x+%2B+8%29%5E2 ALIGN=MIDDLE  ALT=\"56=%28x+%2B+8%29%5E2\"   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=sqrt%2856%29=x+%2B+8 ALIGN=MIDDLE  ALT=\"sqrt%2856%29=x+%2B+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=sqrt%2856%29-8=x+ ALIGN=MIDDLE  ALT=\"sqrt%2856%29-8=x+\"   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=7.48-8=x+ ALIGN=MIDDLE  ALT=\"7.48-8=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=-0.52=x+ ALIGN=MIDDLE  ALT=\"-0.52=x+\"   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=-7.48-8=x+ ALIGN=MIDDLE  ALT=\"-7.48-8=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=-15.48=x+ ALIGN=MIDDLE  ALT=\"-15.48=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=drawing+%28+600%2C+600%2C+-20%2C+10%2C+-60%2C+10%2C+locate%28-8%2C-56%2CV%28-8%2C-56%29%29%2C+circle%28-0.52%2C0%2C0.2%29%2C+circle%28-15.48%2C0%2C0.2%29%2Cgraph%28+600%2C+600%2C+-20%2C+10%2C+-60%2C+10%2C+%28x+%2B+8%29%5E2-56%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );