document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=13406>Question 13406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your help is appreciated.\r<BR>\n" );
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document.write( "Convert equation of the parabola y = -6x^2-6x to standard form and then find the product a x h x k.  \r<BR>\n" );
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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 #6772 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=6772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The \"standard\" form you need for this problem is:\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+-+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( "You can get your equation into this form by \"completing the square\".<BR>\n" );
document.write( "Starting with your equation, factor a (-6), then complete the square in the x-terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6x%5E2+-+6x ALIGN=MIDDLE  ALT=\"y+=+-6x%5E2+-+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor -6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%28x%5E2+%2B+x%29 ALIGN=MIDDLE  ALT=\"y+=+-6%28x%5E2+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square in x by adding the square of half the x-term (1/2)^2 = 1/4 but don't forget that this is multiplied by -6 so you must add -6(1/4)= -3/2 to the other side as well.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+3%2F2+=+-6%28x%5E2+%2B+x+%2B+%281%2F4%29%29 ALIGN=MIDDLE  ALT=\"y+-+3%2F2+=+-6%28x%5E2+%2B+x+%2B+%281%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Factor the parentheses and add 3/2 to both sides.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%28x+%2B+%281%2F2%29%29%5E2+%2B+%283%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+-6%28x+%2B+%281%2F2%29%29%5E2+%2B+%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now compare this with the \"standard\" form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you can see that:\r<BR>\n" );
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document.write( "a = -6,  h = -(1/2), and k = 3/2\r<BR>\n" );
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document.write( "So, to finish the solution to your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ah%2Ak+=+%28-6%29%28-1%2F2%29%283%2F2%29 ALIGN=MIDDLE  ALT=\"a%2Ah%2Ak+=+%28-6%29%28-1%2F2%29%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9/2 = 4.5 </SPAN>\n" );
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