document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389681>Question 389681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> h(t)= c-(d-4t)^2\r<BR>\n" );
document.write( "\n" );
document.write( "At time t=0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t= 2.5, what was the height, in feet, of the ball at time t = 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276216 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=”Garamond” size=”+2”>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ h(t)\ =\ c\ -\ \left(d\ -\ 4t\right)^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand the binomial:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ h(t)\ =\ -16t^2\ +\ 8dt\ +\ c\ -\ d^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Compare this to the standard form of the height function for a projectile near the surface of the Earth with respect to time:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ h(t)\ =\ -16t^2\ +\ v_ot\ +\ h_o\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By comparison you can see that the initial height, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\"> , must be equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\ -\ d^2\">, and the initial velocity, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\ =\ 8d\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know that the maximum height is obtained at the time equal to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">-coordinate of the vertex of the parabola that is the graph of the function.  The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">-coordinate is found by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ t_{max}\ =\ \frac{-8d}{-32}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "but we were given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t_{max}\ =\ 2.5\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From which we can deduce:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ d\ =\ 10\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(verification left as an exercise for the student)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and then we can determine that\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ v_o\ =\ 80\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next we were given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\ =\ 6\">, but knowing that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ 10\ \rightarrow\ d^2\ = 100\">, we can deduce that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ c\ =\ 106\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug in the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ h(t)\ =\ 106\ -\ \left(10\ -\ 4(1)\right)^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And then do the arithmetic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );