document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190141>Question 190141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the equation that goes with a series of plotted points.  The points form what appears to be part of a parabola.  The coordinates given are:\r<BR>\n" );
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document.write( "x     y<BR>\n" );
document.write( "32    6<BR>\n" );
document.write( "48    14<BR>\n" );
document.write( "64    24<BR>\n" );
document.write( "80    38<BR>\n" );
document.write( "96    55<BR>\n" );
document.write( "112   75\r<BR>\n" );
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document.write( "The scenario relates to the speed of a car (x) and the braking distance at that speed (y).  So presumably another coordinate can also be 0,0.\r<BR>\n" );
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document.write( "Given the staring coordinate of 0,0 I have worked out that in the formula form y = ax^2 + bx + c that c = 0, but I cannot work out the procedure to use to solve for a and b and come up with the equation.  I have tried simultaneous equations but think I am doing something wrong.  My boyfriend talked about solving it by taking logs but we have not been taught that way at school.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142714 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=142714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need to find the equation that goes with a series of plotted points. The points form what appears to be part of a parabola. The coordinates given are: <BR>\n" );
document.write( "x y<BR>\n" );
document.write( "32 6<BR>\n" );
document.write( "48 14<BR>\n" );
document.write( "64 24<BR>\n" );
document.write( "80 38<BR>\n" );
document.write( "96 55<BR>\n" );
document.write( "112 75 <BR>\n" );
document.write( "------------<BR>\n" );
document.write( "You are thinking right.<BR>\n" );
document.write( "Use any three of the points to generate 3 equations in a,b,c<BR>\n" );
document.write( "Then solve the system for a,b,c.<BR>\n" );
document.write( "6 = a(6^2) + b(6) + c<BR>\n" );
document.write( "14= a(48^2) + b(48) + c<BR>\n" );
document.write( "24= a(64^2) + 64b + c<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "I used a matrix method to solve the system and found:<BR>\n" );
document.write( "a = 0.00749<BR>\n" );
document.write( "b = -0.21408<BR>\n" );
document.write( "c = 7.01478<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y= 0.00749x^2 - 0.21408x + 7.01478<BR>\n" );
document.write( "=======================================<BR>\n" );
document.write( "I also ran a Quadratic Regression program against<BR>\n" );
document.write( "the whose set of data and came up with:<BR>\n" );
document.write( "y = 0.006x^2-0.2321x+0.6<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "The fact that these answers are not the same means<BR>\n" );
document.write( "that not all the points lie exactly on a parabola.<BR>\n" );
document.write( "That may be what your instructor is trying to show.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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document.write( "need to find the equation that goes with a series of plotted points. The points form what appears to be part of a parabola. The coordinates given are: <BR>\n" );
document.write( "x y<BR>\n" );
document.write( "32 6<BR>\n" );
document.write( "48 14<BR>\n" );
document.write( "64 24<BR>\n" );
document.write( "80 38<BR>\n" );
document.write( "96 55<BR>\n" );
document.write( "112 75 <BR>\n" );
document.write( " </SPAN>\n" );
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