document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029642>Question 1029642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bouncy ball is thrown vertically upward from the ground, after 2 seconds it attains max height of 120 feet, and after 4 seconds it hits the ground.<BR>\n" );
document.write( "On a graph I have my vertex as (2, 120).<BR>\n" );
document.write( "I am trying to find the quadratic equation to represent the path of the ball. t is time of ball in air and s is height of ball at time t.<BR>\n" );
document.write( "I have figured out the equation to be -16t^2+96t=s, then I plug in to the equation t=  (-b ± &#8730;(b^2-4 (a)(c) ))/2a  \r<BR>\n" );
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document.write( "My answers are sorta making sense in relation to my graph, but we are asked to give height of ball at 4 seconds & 6 seconds.  If ball was already on ground at 4 seconds, why are they asking at 6 too?  Not positive I am on the right track.\r<BR>\n" );
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document.write( "Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644602 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=644602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bouncy ball is thrown vertically upward from the ground, after 2 seconds it attains max height of 120 feet, and after 4 seconds it hits the ground.<BR>\n" );
document.write( "On a graph I have my vertex as (2, 120).<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "Since the vertex is at (2,120), -b/(2a) = 2 ; = b = -4a<BR>\n" );
document.write( "120 = a(4) -4a(2) + c<BR>\n" );
document.write( "120 = -4a + c<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Since (4,0) is a point, a(16) + b(4) + c = 0<BR>\n" );
document.write( "16a + 4b + c = 0<BR>\n" );
document.write( "16a + 4(-4a) + c = 0<BR>\n" );
document.write( "c = 0<BR>\n" );
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document.write( "So, 120 = -4a<BR>\n" );
document.write( "a = -30<BR>\n" );
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document.write( "Therefore:: y = -30x^2 + 120x<BR>\n" );
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document.write( "We are asked to give height of ball at 4 seconds & 6 seconds. <BR>\n" );
document.write( "At 4 seconds:<BR>\n" );
document.write( "f(4) = -30(16) + 120(4) = -480 + 480 = 0 (at 4 sec it is on the ground).<BR>\n" );
document.write( "But you knew that.<BR>\n" );
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document.write( "At 6 seconds:<BR>\n" );
document.write( "Well, it is a bouncy ball but you have no info as to the % of rebound,<BR>\n" );
document.write( "so ??????<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( "If ball was already on ground at 4 seconds, why are they asking at 6 too? Not positive I am on the right track.  </SPAN>\n" );
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