document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103985>Question 1103985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward from the top of a<BR>\n" );
document.write( "building 96 feet tall with an initial velocity of 80 feet<BR>\n" );
document.write( "per second. The distance, s (in feet), of the ball from<BR>\n" );
document.write( "the ground after t seconds is given by the function:<BR>\n" );
document.write( "&#119904;(&#119905;) = 96 + 80&#119905; &#8722; 16&#119905;^2\r<BR>\n" );
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document.write( "a.) How long does it take for the ball to reach its<BR>\n" );
document.write( "highest point?\r<BR>\n" );
document.write( "\n" );
document.write( "b.) What is the maximum height the ball reaches?  \r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718709 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of 80 feet per second. The distance, s (in feet), of the ball from the ground after t seconds is given by the function:<BR>\n" );
document.write( "&#55349;&#56416;(&#55349;&#56417;) = 96 + 80&#55349;&#56417; &#8722; 16&#55349;&#56417;^2<BR>\n" );
document.write( "seeing this graphically is helpful<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+10%2C+-50%2C+220%2C+-16x%5E2%2B80x%2B96%2C+196%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-50%2C+220%2C+-16x%5E2%2B80x%2B96%2C+196%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a.) How long does it take for the ball to reach its<BR>\n" );
document.write( "highest point?<BR>\n" );
document.write( "This is a quadratic equation, max occurs on the axis of symmetry x=-b/(2a)<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-80%29%2F%282%2A-16%29%7D%7D%29%0D%0At+=+%7B%7B%7B%28-80%2F%28-32%29 ALIGN=MIDDLE  ALT=\"%28-80%29%2F%282%2A-16%29%7D%7D%29%0D%0At+=+%7B%7B%7B%28-80%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 2.5 seconds<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b.) What is the maximum height the ball reaches? <BR>\n" );
document.write( "Replace t with 2.5 to find s<BR>\n" );
document.write( "s = -16(2.5^2) + 80(2.5) + 96<BR>\n" );
document.write( "s = -16(6.25 )+ 200 + 96<BR>\n" );
document.write( "s = -100 + 296<BR>\n" );
document.write( "s = 196 ft is max height, green line </SPAN>\n" );
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