document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125211>Question 1125211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An object is thrown vertically upward from the ground with a velocity of 96 ft/s. Its height, y, is measured in feet, after t seconds is given by y = 96t - 16t^2. How high will the object be after two seconds? After how many seconds will the object reach its maximum height? What is the maximum height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741517 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=741517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "1.  Substitute 2 for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> and do the arithmetic.\r<BR>\n" );
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document.write( "2.  The graph of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y(t)\"> is a parabola that opens downward because the lead coefficient, -16, is less than zero.  Therefore the maximum value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> will be at the vertex of the parabola.  The vertex occurs at the point calculated by dividing the opposite of the linear term by twice the lead coefficient. So for\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "The vertex is at:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (-\frac{b}{2a},f\(-\frac{b}{2a}\)\)\">\r<BR>\n" );
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document.write( "You need the abscissa of this point, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{b}{2a}\">, to answer \"After how many seconds...\" and the ordinate, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f\(-\frac{b}{2a}\)\">, of the point to answer \"What is the maximum...\"\r<BR>\n" );
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document.write( "This might make more sense if you put your function into standard form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(t)\ =\ -16t^2\ +\ 96t\">\r<BR>\n" );
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document.write( "so that it is clear that 1: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> is a function of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> and 2: the lead coefficient is -16 and the linear term coefficient is 96]\r<BR>\n" );
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document.write( "You might also want to note that for this model to be an accurate representation of a physical phenomenon, the object must be touching the ground when it was launched with a 96 feet per second upward initial velocity.<BR>\n" );
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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( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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