document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162781>Question 1162781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is tossed into the air so that the height after 1, 2, and 4 seconds is as given in the following table. If the relationship between the height of the ball h and the time t is quadratic, then the relationship can be written as:<BR>\n" );
document.write( "h=at^2+bt+c <BR>\n" );
document.write( "Use the information in the table to write a system of three equations in three variables a, b, and c. Solve the system to find the exact relationship between h and t.\r<BR>\n" );
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document.write( "t	h<BR>\n" );
document.write( "1	144<BR>\n" );
document.write( "2	128<BR>\n" );
document.write( "4	0<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 #786658 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a+b+c=144<BR>\n" );
document.write( "16a+4b+c=0\r<BR>\n" );
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document.write( "c=144-a-b=-16a-4b<BR>\n" );
document.write( "15a+3b=-144<BR>\n" );
document.write( "divide by 3<BR>\n" );
document.write( "5a+b=-48\r<BR>\n" );
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document.write( "also 4a+2b+c=128<BR>\n" );
document.write( "c=128-4a-2b=-16a-4b<BR>\n" );
document.write( "12a+2b=-128<BR>\n" );
document.write( "6a+b=-64<BR>\n" );
document.write( "add to that -5a-b=-48<BR>\n" );
document.write( "a=-16, which is reassuring, since -16t^2 is the leading coefficient in English units.<BR>\n" );
document.write( "b is 32<BR>\n" );
document.write( "c=128\r<BR>\n" );
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document.write( "h=-16t^2+32t+128<BR>\n" );
document.write( "which is something thrown off a 128 foot high building at 32 ft/sec upward velocity.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-125%2C150%2C-16x%5E2%2B32x%2B128%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-125%2C150%2C-16x%5E2%2B32x%2B128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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