document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437300>Question 437300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Suppose you are in the stands of a World Series baseball game.  A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air.  \r<BR>\n" );
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document.write( "When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation.  \r<BR>\n" );
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document.write( "			  height=-16t^2+96t+5\r<BR>\n" );
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document.write( "	a. Does the graph of this equation open up or down? How did you determine this? The ball graph of the equation opened down ward. I determined this because the coefficient of the highest power is negative. <BR>\n" );
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document.write( "b. Describe how the ball travels – what is the shape of its path? the path that the ball travels is upward into the air and bows slightly  when returning downward.\r<BR>\n" );
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document.write( "c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.\r<BR>\n" );
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document.write( "Note. Your answer, t, will be in terms of seconds.\r<BR>\n" );
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document.write( "d. After how many seconds will the ball reach its maximum height? <BR>\n" );
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document.write( "e. What is the height that the ball will reach? <BR>\n" );
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document.write( "f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e? <BR>\n" );
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document.write( "g. How many solutions are there to the equation ? How do you know? <BR>\n" );
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document.write( "h. What do the solutions represent? Is there a solution that does not make sense? Why?\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 #302483 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=302483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Suppose you are in the stands of a World Series baseball game. A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air. <BR>\n" );
document.write( "When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation. <BR>\n" );
document.write( "height=-16t^2+96t+5 <BR>\n" );
document.write( "a. Does the graph of this equation open up or down? How did you determine this? The ball graph of the equation opened down ward. I determined this because the coefficient of the highest power is negative. \r<BR>\n" );
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document.write( "b. Describe how the ball travels – what is the shape of its path? the path that the ball travels is upward into the air and bows slightly when returning downward. <BR>\n" );
document.write( "c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.<BR>\n" );
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document.write( "Solve: -16t^2+96t+5 = 0<BR>\n" );
document.write( "t = [-96+-sqrt(96^2-4*-16*5)]/-32<BR>\n" );
document.write( "t = [-96+-sqrt(9536)]/-32<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "t = 6.05 seconds <BR>\n" );
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document.write( "Note. Your answer, t, will be in terms of seconds.<BR>\n" );
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document.write( "d. After how many seconds will the ball reach its maximum height? <BR>\n" );
document.write( "max occurs when t = -b/(2a) = -96/(2*-16) = 3 seconds<BR>\n" );
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document.write( "e. What is the height that the ball will reach?<BR>\n" );
document.write( "Solve for h(3)= 149 ft.<BR>\n" );
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document.write( "f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e? <BR>\n" );
document.write( "Ans: (3,149)<BR>\n" );
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document.write( "g. How many solutions are there to the equation ? How do you know? <BR>\n" );
document.write( "Ans: 2<BR>\n" );
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document.write( "h. What do the solutions represent? <BR>\n" );
document.write( "Time when the height of the ball is zero.<BR>\n" );
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document.write( "Is there a solution that does not make sense?<BR>\n" );
document.write( "Yes<BR>\n" );
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document.write( " Why?<BR>\n" );
document.write( "t is negative.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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