document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993171>Question 993171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help I do not understand any of these questions. These are all quadratic formulas. Please show all work it helps me learn how to do the questions step by step.\r<BR>\n" );
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document.write( "1.	Imagine yourself standing on the roof of the 1450-foot Sears Tower in Chicago.  When you throw a baseball upward from the roof of the tower, the ball’s height above the ground, H (in feet), can be described as a function of the time, t (in seconds), since the ball was dropped.  This height function is defined by <BR>\n" );
document.write( "H(t) = -16t2 + 80t +1450\r<BR>\n" );
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document.write( "a.	Identify the vertical intercept and  what does it mean in the context of the problem\r<BR>\n" );
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document.write( "b.	After the baseball is thrown, how long will the ball hit the ground?\r<BR>\n" );
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document.write( "c.	Your answer to question #2 identifies one horizontal intercept of the equation.  Identify another horizontal intercept and discuss whether it makes sense in the context of the problem.\r<BR>\n" );
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document.write( "d.	Find the vertex of the equation and interpret it meaning in the context of the problem.\r<BR>\n" );
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document.write( "e.	How far from the ground is the ball after 8 seconds?\r<BR>\n" );
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document.write( "f.	At what time(s) is the ball 1500 feet above the ground?\r<BR>\n" );
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document.write( "g.	Identify the practical domain in the context of the problem.\r<BR>\n" );
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document.write( "h.	Identify the practical range in the context of the problem.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612537 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation H(t) = -16t^2 + 80t +1450  describes a parabola that opens downward<BR>\n" );
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document.write( "a) at time t = 0, H(0) = 1450, 1450 is the vertical intercept and says that the ball is 1450 feet above the ground at time t = 0<BR>\n" );
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document.write( "b) we must solve the quadratic for t when H(t) = 0, that is<BR>\n" );
document.write( "-16t^2 + 80t +1450 = 0<BR>\n" );
document.write( "divide both sides of = by -2<BR>\n" );
document.write( "8t^2 - 40t - 725 = 0<BR>\n" );
document.write( "use quadratic formula to solve for t<BR>\n" );
document.write( "t = (40 + sqrt((-40^2) - 4*8*(-725)))/(2*8) = 12.342509843 approx 12.343<BR>\n" );
document.write( "t = (40 - sqrt((-40^2) - 4*8*(-725)))/(2*8) = &#8722;7.342509843 approx -7.343<BR>\n" );
document.write( "it takes 12.343 seconds before the ball hits the ground<BR>\n" );
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document.write( "c) the other horizontal intercept is -7.343, we can not have negative time<BR>\n" );
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document.write( "d) the t for the vertex is given by the following formula<BR>\n" );
document.write( "t = -b / 2a, then<BR>\n" );
document.write( "t = -80 / 2(-16) = 2.5<BR>\n" );
document.write( "now substitute t = 2.5 in the H(t) equation<BR>\n" );
document.write( "H(t) = -16t^2 + 80t +1450 <BR>\n" );
document.write( "H(2.5) = -16(2.5)^2 + 80(2.5) + 1450<BR>\n" );
document.write( "H(2.5) = 1550<BR>\n" );
document.write( "the vertex is (2.5, 1550), this tells us that at time 2.5 seconds the ball reaches its maximum height of 1550 feet<BR>\n" );
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document.write( "e) H(8) = -16(8)^2 + 80(8) + 1450<BR>\n" );
document.write( "H(8) = 1066<BR>\n" );
document.write( "after 8 seconds the ball is 1066 feet from the ground<BR>\n" );
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document.write( "f) at time 2.5 seconds the ball is 1550 feet above the ground<BR>\n" );
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document.write( "g) practical domain is t values from 0 to 12.343<BR>\n" );
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document.write( "h) practical range is height values from 0 to 1550<BR>\n" );
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