document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637369>Question 637369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height of a soccer ball that is kicked from the ground can<BR>\n" );
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document.write( "be approximated by the function:<BR>\n" );
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document.write( " y = -16&#8901;x2 + 80&#8901;x<BR>\n" );
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document.write( " where y is the height of the soccer ball in feet x seconds after it is kicked.<BR>\n" );
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document.write( "Find the time it takes the soccer ball to reach its maximum height:       seconds<BR>\n" );
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document.write( "What is the soccer ball’s maximum height:       feet<BR>\n" );
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document.write( "Find the time it takes from the moment the soccer ball is kicked until it returns to the ground:         seconds<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 #401610 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of a soccer ball that is kicked from the ground can be approximated by the function:<BR>\n" );
document.write( "y = -16x^2 + 80x<BR>\n" );
document.write( "where y is the height of the soccer ball in feet x seconds after it is kicked.<BR>\n" );
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document.write( "Find the time it takes the soccer ball to reach its maximum height: seconds<BR>\n" );
document.write( "Vertex of parabola is the max.<BR>\n" );
document.write( "Time when it hits the max is at the \"axis of symmetry\":<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -80/(2(-16))<BR>\n" );
document.write( "x = -40/(-16)<BR>\n" );
document.write( "x = 40/16<BR>\n" );
document.write( "x = 2.5 seconds<BR>\n" );
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document.write( "What is the soccer ball’s maximum height: feet<BR>\n" );
document.write( "plug the value of x found above back into the original equation:<BR>\n" );
document.write( "y = -16x^2 + 80x<BR>\n" );
document.write( "y = -16(2.5)^2 + 80(2.5)<BR>\n" );
document.write( "y = 100 feet<BR>\n" );
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document.write( "Find the time it takes from the moment the soccer ball is kicked until it returns to the ground: seconds<BR>\n" );
document.write( "set y to zero and solve for x:<BR>\n" );
document.write( "y = -16x^2 + 80x<BR>\n" );
document.write( "0 = -16x^2 + 80x<BR>\n" );
document.write( "0 = -16x(x - 5)<BR>\n" );
document.write( "x = {0, 5}<BR>\n" );
document.write( "0 is when it was first kicked<BR>\n" );
document.write( "so the answer is<BR>\n" );
document.write( "x = 5 seconds<BR>\n" );
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