document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128653>Question 1128653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi can you plz help me with this qs? I didn't know under which section to post it so im posting it here:<BR>\n" );
document.write( "the curve y = ax^3 + bx^2 + cx + d has a gradient of -3 at (0, 15/2) and a turning point at (3,6). Find a,b,c,d <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 #745144 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=745144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "y = ax^3+bx^2+cx+d<BR>\n" );
document.write( "y' = 3ax^2+2bx+c<BR>\n" );
document.write( "y'' = 6ax+2b<br><BR>\n" );
document.write( "The given information tells us...<br><BR>\n" );
document.write( "y(0) = 15/2  -->  c = 15/2  (1)<BR>\n" );
document.write( "y(3) = 6  -->  27a+9b+3c+d = 6 (2)<BR>\n" );
document.write( "y'(0) = -3  -->  c = -3  (3)<BR>\n" );
document.write( "y''(3) = 0  -->  18a+2b = 0  (4)<br><BR>\n" );
document.write( "Substitute (1) and (3) in (2):<br><BR>\n" );
document.write( "27a+9b-9+15/2 = 6<BR>\n" );
document.write( "27a+9b = 15/2<BR>\n" );
document.write( "18a+6b = 5 (5)<br><BR>\n" );
document.write( "Subtract (4) from (5):<br><BR>\n" );
document.write( "4b = 5<BR>\n" );
document.write( "b = 5/4  (6)<br><BR>\n" );
document.write( "Substitute (6) in (4):<br><BR>\n" );
document.write( "18a+5/2 = 0<BR>\n" );
document.write( "a = -5/36<br><BR>\n" );
document.write( "The polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2F36%29x%5E3%2B%285%2F4%29x%5E2-3x%2B%2815%2F2%29 ALIGN=MIDDLE  ALT=\"%28-5%2F36%29x%5E3%2B%285%2F4%29x%5E2-3x%2B%2815%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C10%2C-2%2C10%2C%28-5%2F36%29x%5E3%2B%285%2F4%29x%5E2-3x%2B%2815%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );