document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118862>Question 118862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the procedures to write a quadratic equation in vertex form? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86977 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=86977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Follow these steps to convert a parabola from <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"f%28x%29=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >    \r<BR>\n" );
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document.write( "1. Factor out an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the first two terms, and leave a space inside.<BR>\n" );
document.write( " <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+_%29+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+_%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
document.write( "2. Multiply the coefficient 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;\" > term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%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=%281%2F2%29%28b%2Fa%29+=+b%2F2a ALIGN=MIDDLE  ALT=\"%281%2F2%29%28b%2Fa%29+=+b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   <BR>\n" );
document.write( "3. Square this term and add it to the space we made.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( " 4. Now, we have upset the balance of the equation. We <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=added+ ALIGN=MIDDLE  ALT=\"added+\"   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=%28b%2F2a%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28b%2F2a%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28b%2F2a%29%5E2%29 ALIGN=MIDDLE  ALT=\"a%28b%2F2a%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which we need to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=subtract ALIGN=MIDDLE  ALT=\"subtract\"   DISABLED_style= \"max-width:90%; height:auto;\" > in order to keep the balance of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c+-+a%28b%2F2a%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+a+%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29+%2B+c+-+a%28b%2F2a%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "5. Now, we can write the part that is in parentheses <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  as \r<BR>\n" );
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document.write( "	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B++b%2F2a%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28x%2B++b%2F2a%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " This is why we did all of the above steps.<BR>\n" );
document.write( "   <BR>\n" );
document.write( "	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a+%28x%2B++b%2F2a%29%5E2+%2B+c+-+a%28b%2F2a%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+a+%28x%2B++b%2F2a%29%5E2+%2B+c+-+a%28b%2F2a%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "   6. Rewrite the terms and simplify a bit. The reason for this will become apparent later on.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+a%28x-%28-b%2F2a%29%29%2B+%284ac-b%5E2%29%2F4a ALIGN=MIDDLE  ALT=\"f%28x%29=+a%28x-%28-b%2F2a%29%29%2B+%284ac-b%5E2%29%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >    \r<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "   7. Now, let’s simply things by calling \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-%28b%2F2a%29 ALIGN=MIDDLE  ALT=\"h=-%28b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%284ac-b%5E2%29%2F4a ALIGN=MIDDLE  ALT=\"k+=+%284ac-b%5E2%29%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"f%28x%29=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <BR>\n" );
document.write( "    \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );