document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=904410>Question 904410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Do I have this quadratic to standard form problem correct?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #548673 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=548673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> unfortunately no.\r<BR>\n" );
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document.write( "let me show you how to do it and you should be able to see where you went wrong.\r<BR>\n" );
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document.write( "start with g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+30x+%2B+55 ALIGN=MIDDLE  ALT=\"5x%5E2+-+30x+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "factor out the 5 to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x%5E2+-+6x+%2B+11%29 ALIGN=MIDDLE  ALT=\"5%2A%28x%5E2+-+6x+%2B+11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "complete the square within the parentheses to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28%28x-3%29%5E2-9%2B11%29 ALIGN=MIDDLE  ALT=\"5%2A%28%28x-3%29%5E2-9%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify by applying the distributive law of multiplication to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+-+5%2A9+%2B+5%2A11 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+-+5%2A9+%2B+5%2A11\"   DISABLED_style= \"max-width:90%; height:auto;\" > which can be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+-+45+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+-+45+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "simplify further by combining like terms to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+%2B+10 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to determine if the standard form is equivalent to your original form, then simply pick a value of x at random and solve each of the equations for that value of x.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 20, the original equation becomes g(20) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A20%5E2+-30%2A20 ALIGN=MIDDLE  ALT=\"5%2A20%5E2+-30%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 55 which becomes g(20) = 1455.\r<BR>\n" );
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document.write( "when x = 20, the standard form equation becomes (g(20) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A15%2820-3%29%5E2%2B10 ALIGN=MIDDLE  ALT=\"5%2A15%2820-3%29%5E2%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes g(20) = 1455.\r<BR>\n" );
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document.write( "both forms give you the same answer which is a good indication that you translates correctly.\r<BR>\n" );
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document.write( "factoring by completing the square is tricky until you get the hang of it.\r<BR>\n" );
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document.write( "you have to do a few before you become comfortable with it.\r<BR>\n" );
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document.write( "some instructions will have you separate out the constant term.\r<BR>\n" );
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document.write( "it winds up being the same thing with perhaps one less computation.\r<BR>\n" );
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document.write( "let me do it that way so you can see how it's done.\r<BR>\n" );
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document.write( "start with g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+30x+%2B+55 ALIGN=MIDDLE  ALT=\"5x%5E2+-+30x+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" > as before.\r<BR>\n" );
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document.write( "separate the x terms and the constant terms so  they will be shown separately as follows:\r<BR>\n" );
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document.write( "g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2+-+30x%29+%2B+55 ALIGN=MIDDLE  ALT=\"%285x%5E2+-+30x%29+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the 5x^2 - 30x has been enclosed in a set of parentheses to group those terms together.\r<BR>\n" );
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document.write( "now factor out the 5 from the x terms to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x%5E2+-+6x%29+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28x%5E2+-+6x%29+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now take half of the coefficient of the x term and complete the squares to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+-+9%29+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+-+9%29+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "why did you have to subtract the 9?\r<BR>\n" );
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document.write( "before we go through that, the 9 is the result of half the coefficient of the x term squared.\r<BR>\n" );
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document.write( "when you take x^2 - 6x and take half the coefficient of the x term and replace it with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+=+x%5E2+-+6x+%2B+9 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+=+x%5E2+-+6x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "this means you have 9 more than you wanted.\r<BR>\n" );
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document.write( "the 9 happens to be half of the coefficient of the x term squared.\r<BR>\n" );
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document.write( "so you subtract 9 and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+-+9 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+%2B+9+-+9 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+%2B+9+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x ALIGN=MIDDLE  ALT=\"x%5E2+-+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is what you want.\r<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+6x%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%5E2+-+9%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%5E2+-+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "all of that stays within the parentheses.\r<BR>\n" );
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document.write( "you started with g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x%5E2+-+6x%29+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28x%5E2+-+6x%29+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you ended up with g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28%28x-3%29%5E2+-+9%29+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28%28x-3%29%5E2+-+9%29+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "now you want to remove the parentheses by applying the distributive law of multiplication to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+-+45+%2B+55 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+-+45+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "now you want to simplify further by combining like terms to get g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29%5E2+%2B+10 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29%5E2+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "same answer as before except you didn't factor out the 5 from the constant term.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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