document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187434>Question 1187434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a toy car was made to run the length of a room. Suppose its speed increase so that it ran 1 meter the first minute, 2 meters in the second minute, 3 meters in the third minute, and so on. The speed is increasing about 1 meter each minute. The relation between the distance of the toy car from the starting point and the number of minutes it has run is shown below\r<BR>\n" );
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document.write( "time (X)     0    1 2    3     4<BR>\n" );
document.write( "distance (y) 0    1 3    6     10\r<BR>\n" );
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document.write( "1. Determine the equation with the given table of values<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 #818593 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It's hard to know how to respond, since we have no idea of your level of mathematical knowledge....<br><BR>\n" );
document.write( "Following is one way to find the equation giving the number of meters as a function of the number of minutes.<br><BR>\n" );
document.write( "If you don't understand this method, re-post the question, indicating what level of math you have studied (algebra I, algebra II, pre-calculus, etc.).<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1   3   6  10  distances in meters after 1, 2, 3, and 4 minutes\r\n" );
document.write( "  2   3   4    \"first differences\"\r\n" );
document.write( "    1   1      \"second differences\"</PRE><BR>\n" );
document.write( "The constant second differences tell us the equation is quadratic -- of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use f(1)=1, f(2)=3, and f(3)=6 to form three equations that can be solved to find the coefficients a, b, and c and thus find the equation.<br><BR>\n" );
document.write( "f(1): a+b+c=1  [1]<BR>\n" );
document.write( "f(2): 4a+2b+c=3  [2]<BR>\n" );
document.write( "f(3): 9a+3b+c=6  [3]<br><BR>\n" );
document.write( "[3]-[2]: 5a+b=3  [4]<BR>\n" );
document.write( "[2]-[1]: 3a+b=2  [5]<br><BR>\n" );
document.write( "[4]-[5]: 2a=1; a=1/2  [6]<br><BR>\n" );
document.write( "Substitute [6] in [5]: 3/2+b=2; b=1/2  [7]<br><BR>\n" );
document.write( "Substitute [6] and [7] in [1]: 1/2+1/2+c=1; c=0<br><BR>\n" );
document.write( "The coefficients are<BR>\n" );
document.write( "a=1/2<BR>\n" );
document.write( "b=1/2<BR>\n" );
document.write( "c=0<br><BR>\n" );
document.write( "ANSWER: The equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%281%2F2%29x%5E2%2B%281%2F2%29%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%281%2F2%29x%5E2%2B%281%2F2%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or, in other possible forms,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%281%2F2%29%28x%5E2%2Bx%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%281%2F2%29%28x%5E2%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%281%2F2%29%28x%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%281%2F2%29%28x%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );