document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549395>Question 549395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert Standard equations to vertex form:<BR>\n" );
document.write( "-3x^2-60x-294<BR>\n" );
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document.write( "*Step by step </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357724 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The quadratic function, or equation of a parabola (whichever way you want to see it)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3x%5E2-60x-294 ALIGN=MIDDLE  ALT=\"f%28x%29=-3x%5E2-60x-294\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%5E2-60x-294 ALIGN=MIDDLE  ALT=\"y=-3x%5E2-60x-294\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "can be transformed into the vertex form in steps, using facts of algebra you learned before.<BR>\n" );
document.write( "You can also calculate the coordinates of the vertex from formulas in your textbook, and then plug those coordinates into another formula from your textbook to get the vertex form.<BR>\n" );
document.write( "The steps, go like this:<BR>\n" );
document.write( "I want all the terms with x, and only the terms with x on the right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%5E2-60x-294 ALIGN=MIDDLE  ALT=\"y=-3x%5E2-60x-294\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B294=-3x%5E2-60x ALIGN=MIDDLE  ALT=\"y%2B294=-3x%5E2-60x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I added 294 to each side)<BR>\n" );
document.write( "I don't want a coefficient, or factor, or minus sign, directly in front of <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B294=-3x%5E2-60x ALIGN=MIDDLE  ALT=\"y%2B294=-3x%5E2-60x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B294=-3%28x%5E2%2B20x%29 ALIGN=MIDDLE  ALT=\"y%2B294=-3%28x%5E2%2B20x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, extracting common factor (-3).<BR>\n" );
document.write( "At this point, it's time to \"complete the square\".<BR>\n" );
document.write( "The right side parenthesis reminds me of the square of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-10%29 ALIGN=MIDDLE  ALT=\"%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-10%29%5E2=x%5E2-20x%2B100 ALIGN=MIDDLE  ALT=\"%28x-10%29%5E2=x%5E2-20x%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so I decide to add to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-300=-3%2A100 ALIGN=MIDDLE  ALT=\"-300=-3%2A100\"   DISABLED_style= \"max-width:90%; height:auto;\" > or, if you prefer,<BR>\n" );
document.write( "I'll subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300=3%2A100 ALIGN=MIDDLE  ALT=\"300=3%2A100\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B294-300=-3%28x%5E2%2B20x%29-3%2A100 ALIGN=MIDDLE  ALT=\"y%2B294-300=-3%28x%5E2%2B20x%29-3%2A100\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B294-300=-3%28x%5E2%2B20x%2B100%29 ALIGN=MIDDLE  ALT=\"y%2B294-300=-3%28x%5E2%2B20x%2B100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I can write what's in parentheses as the square I know it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=-3%28x%2B10%29%5E2 ALIGN=MIDDLE  ALT=\"y-6=-3%28x%2B10%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I also simplified the left hand side, at the same time).<BR>\n" );
document.write( "NOTE: (That is not yet what most call the vertex form, but it shows that it is the parabola that results from modifying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by flipping it upside down, stretching it vertically to 3 times its size, shifting it to the left 10 units and shifting it up 6 units).<BR>\n" );
document.write( "LAST STEP: Add 6 to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=-3%28x%2B10%29%5E2 ALIGN=MIDDLE  ALT=\"y-6=-3%28x%2B10%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%28x%2B10%29%5E2%2B6 ALIGN=MIDDLE  ALT=\"y=-3%28x%2B10%29%5E2%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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