document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884252>Question 884252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hey! <BR>\n" );
document.write( "I am having a lot of trouble with my year 12 maths and was wondering if anyone was able to assist! <BR>\n" );
document.write( "the problem solving question I have been given with, shows a table of variables being <BR>\n" );
document.write( "x | 0  | 1 | 2 |  3 |  4  |<BR>\n" );
document.write( "y | -3 | 0 | 5 | 12 | 21 |<BR>\n" );
document.write( "for this, it then explains the first and second difference between these numbers <BR>\n" );
document.write( "I understand this as the first difference is<BR>\n" );
document.write( "between -3 and 5 the difference = 3  between and 0 and 5 the difference = 5, between 5 and 12 the difference = 7, and between 12 and 21 the difference = 9\r<BR>\n" );
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document.write( "the second difference then being the difference between these first difference numbers,<BR>\n" );
document.write( "3 and 5 = 2<BR>\n" );
document.write( "5 and 7 = 2<BR>\n" );
document.write( "7 and 9 = 2<BR>\n" );
document.write( "I also understand these are all constant. <BR>\n" );
document.write( "so, the question has given us the rule of y=ax^2 + bx + c which I know is a general function\r<BR>\n" );
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document.write( "it then explains that the first row of entries is obtained by substituting the x values into the rule and said that when x = 1 you just substitute that into the equation. being -> y=a(1) + b(1) + c<BR>\n" );
document.write( "which then simplifies into a + b + c\r<BR>\n" );
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document.write( "the next part then says that the second row of entries (or the first difference in the pattern) is obtained by subtracting consecutive entries in the first row\r<BR>\n" );
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document.write( "my first question being - what and where are the consecutive entries ?<BR>\n" );
document.write( "my second question being that the example then substitutes to <BR>\n" );
document.write( "4a + 2b + c - (a + b + c) = 3a + b \r<BR>\n" );
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document.write( "I am unsure of where these substitutions (being the 4a and 2b) have come from ? \r<BR>\n" );
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document.write( "sorry for the very long explanation but I would be very grateful for an answer! <BR>\n" );
document.write( "thank you for you're time <BR>\n" );
document.write( ":) <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534112 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=a%280%29%5E2%2Bb%280%29%2Bc ALIGN=MIDDLE  ALT=\"-3=a%280%29%5E2%2Bb%280%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-3 ALIGN=MIDDLE  ALT=\"c=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now you already know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%281%29%5E2%2Bb%281%29-3 ALIGN=MIDDLE  ALT=\"0=a%281%29%5E2%2Bb%281%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=3 ALIGN=MIDDLE  ALT=\"a%2Bb=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5 ALIGN=MIDDLE  ALT=\"y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=a%282%29%5E2%2Bb%282%29-3 ALIGN=MIDDLE  ALT=\"5=a%282%29%5E2%2Bb%282%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=8 ALIGN=MIDDLE  ALT=\"4a%2B2b=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb=4 ALIGN=MIDDLE  ALT=\"2a%2Bb=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you have two equations in two unknowns and you should be able to solve.<BR>\n" );
document.write( "Subtract eq. 1 from eq. 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb-a-b=4-3 ALIGN=MIDDLE  ALT=\"2a%2Bb-a-b=4-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now back substitute to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bb=3 ALIGN=MIDDLE  ALT=\"1%2Bb=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now you have all three values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=x%5E2%2B2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );