document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151718>Question 151718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you write y=-4x^2+8x-1 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 #111535 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=111535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%5E2%2B8x-1 ALIGN=MIDDLE  ALT=\"y=-4x%5E2%2B8x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in vertex form, we need to complete the square. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B8x-1 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B8x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x%5E2-2x%2B1%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28x%5E2-2x%2B1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This step is very important, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <font size=4><b>must</b></font> be equal to 1.\r<BR>\n" );
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document.write( "Take half 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;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28-2%29=-1 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-2%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2=%28-1%29%28-1%29=1 ALIGN=MIDDLE  ALT=\"%28-1%29%5E2=%28-1%29%28-1%29=1\"   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=-4%28x%5E2-2x%2Bhighlight%281-1%29%2B1%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28x%5E2-2x%2Bhighlight%281-1%29%2B1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <font size=4><b>and</b></font> subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the parenthesis. Make sure to place this after the \"x\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1=0 ALIGN=MIDDLE  ALT=\"1-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the expression is not changed.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28%28x%5E2-2x%2B1%29-1%2B1%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28%28x%5E2-2x%2B1%29-1%2B1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the first three terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28%28x-1%29%5E2-1%2B1%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28%28x-1%29%5E2-1%2B1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%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=-4%28%28x-1%29%5E2-3%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28%28x-1%29%5E2-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-1%29%5E2-4%28-3%2F4%29 ALIGN=MIDDLE  ALT=\"-4%28x-1%29%5E2-4%28-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-1%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"-4%28x-1%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "So after completing the square, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B8x-1 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B8x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-1%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"-4%28x-1%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B8x-1=-4%28x-1%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B8x-1=-4%28x-1%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%5E2%2B8x-1 ALIGN=MIDDLE  ALT=\"y=-4x%5E2%2B8x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%28x-1%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"y=-4%28x-1%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%28x-1%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"y=-4%28x-1%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is now in vertex form <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=a=-4 ALIGN=MIDDLE  ALT=\"a=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1 ALIGN=MIDDLE  ALT=\"h=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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