document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287399>Question 287399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My problem is:Identify the completing the squares, the vertex, the y-intercept and the axis of symmetry.\r<BR>\n" );
document.write( "\n" );
document.write( "1. y=x^2+6x-11<BR>\n" );
document.write( "2. y=3x^2-x+4<BR>\n" );
document.write( "3. y=2x^2+7x-3<BR>\n" );
document.write( "4. y=2x^2-8x-12\r<BR>\n" );
document.write( "\n" );
document.write( "I need step by step answers\r<BR>\n" );
document.write( "\n" );
document.write( "my email address is gdkpw@hotmail.com<BR>\n" );
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 #208286 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The best way to think of it is:<BR>\n" );
document.write( "The axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+k ALIGN=MIDDLE  ALT=\"x+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is midway between the roots of the equation.<BR>\n" );
document.write( "Then you find the vertex by plugging in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "back into the equation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Cy ALIGN=MIDDLE  ALT=\"x%2Cy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the vertex.<BR>\n" );
document.write( "An easy formula is: if the equation is in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the axis of symmetry is at<BR>\n" );
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" );
document.write( "The y-intercept is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+c ALIGN=MIDDLE  ALT=\"y+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "I'll do your 1st problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2B+6x+-+11 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2B+6x+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The y-intercept is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-11 ALIGN=MIDDLE  ALT=\"y+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now find roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x++-+11+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x++-+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+=+11 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+%2B+%286%2F2%29%5E2+=+11+%2B+%286%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+%2B+%286%2F2%29%5E2+=+11+%2B+%286%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+%2B+9+=+11+%2B+9 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+%2B+9+=+11+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%5E2+=+20 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3+=+sqrt%2820%29 ALIGN=MIDDLE  ALT=\"x+%2B+3+=+sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3+%2B-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"x+=+-3+%2B-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The axis of symmetry is midway between the 2 roots which are:<BR>\n" );
document.write( "root1 =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+%2B+sqrt%2820%29 ALIGN=MIDDLE  ALT=\"+-3+%2B+sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "root2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+-+sqrt%2820%29 ALIGN=MIDDLE  ALT=\"-3+-+sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is midway between these roots, so<BR>\n" );
document.write( "<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;\" > is the axis of symmetry<BR>\n" );
document.write( "And the simple formula <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;\" > gives the same answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+6 ALIGN=MIDDLE  ALT=\"b+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+-6%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "Now plug this result back into the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2B+6x+-+11 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2B+6x+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-3%29%5E2+%2B+6%2A%28-3%29+-+11 ALIGN=MIDDLE  ALT=\"y+=+%28-3%29%5E2+%2B+6%2A%28-3%29+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9+-+18+-+11 ALIGN=MIDDLE  ALT=\"y+=+9+-+18+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-20 ALIGN=MIDDLE  ALT=\"y+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the vertex is at (-3,-20)<BR>\n" );
document.write( "I'll plot the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+x%5E2+%2B+6x+-+11%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+x%5E2+%2B+6x+-+11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );