document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199164>Question 1199164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a ball thrown verticaly into the air such that its height can be described by the following function h(t)=16t2 +48t+6  where t is the time (in seconds) since the ball was thrown and h (t) is the heigth of the ball (in feet) above the ground.  a)at what time does the ball reach its maximun height       seconds  b)what is the maximum height     feet       c)  when does the ball hit the ground (round to the nearest hundreth)        seconds.  d) what is h (2)    h(2)=         e) interpret what the ordered pair (3,6)means in the context of the problem. use a complete sentence in your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832883 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I have a feeling the function should be<BR>\n" );
document.write( "h(t) = -16t^2 + 48t + 6<BR>\n" );
document.write( "where the 16 is negative up front.\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "I'll use x in place of t, and y in place of h(t).\r<BR>\n" );
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document.write( "The equation turns into<BR>\n" );
document.write( "y = -16x^2 + 48x + 6<BR>\n" );
document.write( "Compare this to <BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "to find that<BR>\n" );
document.write( "a = -16<BR>\n" );
document.write( "b = 48<BR>\n" );
document.write( "c = 6\r<BR>\n" );
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document.write( "We'll use the first two values to compute the following:<BR>\n" );
document.write( "h = -b/(2a) <BR>\n" );
document.write( "h = -48/(2*(-16)) <BR>\n" );
document.write( "h = 1.5<BR>\n" );
document.write( "This is the x coordinate of the vertex (h,k).\r<BR>\n" );
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document.write( "Answer: The ball reaches max height at <font color=red>1.5 seconds</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Use the previous result to find the y coordinate of the vertex.<BR>\n" );
document.write( "y = -16x^2 + 48x + 6<BR>\n" );
document.write( "y = -16(1.5)^2 + 48(1.5) + 6<BR>\n" );
document.write( "y = 42<BR>\n" );
document.write( "The vertex is located at (h,k) = (1.5, 42).<BR>\n" );
document.write( "This represents the highest point of this parabola.\r<BR>\n" );
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document.write( "Answer: The max height of the ball is <font color=red>42 feet</font>\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Replace y with 0 and solve for x.<BR>\n" );
document.write( "y = -16x^2 + 48x + 6<BR>\n" );
document.write( "0 = -16x^2 + 48x + 6<BR>\n" );
document.write( "-16x^2 + 48x + 6 = 0<BR>\n" );
document.write( "-2(8x^2 - 24x - 3) = 0<BR>\n" );
document.write( "8x^2 - 24x - 3 = 0\r<BR>\n" );
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document.write( "We plug these values into the quadratic formula<BR>\n" );
document.write( "a = 8<BR>\n" );
document.write( "b = -24<BR>\n" );
document.write( "c = -3<BR>\n" );
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document.write( "The steps in your homework do not to be as verbose as what I've described above. <BR>\n" );
document.write( "You can skip a few steps.<BR>\n" );
document.write( "The decimal values are approximate.<BR>\n" );
document.write( "Ignore the negative x solution because a negative time value makes no sense. \r<BR>\n" );
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document.write( "Answer: The ball hits the ground at <font color=red>approximately 3.12 seconds</font>\r<BR>\n" );
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document.write( "I'll let the student handle parts (d) and (e).<BR>\n" );
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