document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005442>Question 1005442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  What is the maximum height that a basketball will have if thrown up into the air from a height of six feet, with an initial speed of 20 feet per second?  (Must use quadratic formula).\r<BR>\n" );
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document.write( " 2.  After how many seconds does the basketball hit the ground?  (Must solve by completing the square)\r<BR>\n" );
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document.write( "Thank you anyone for helping me.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621713 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> quadratic formula for height at time t is<BR>\n" );
document.write( "s(t) = -gt^2 + vot + ho, where g is force of gravity, vo is the objects initial velocity, and ho is initial height<BR>\n" );
document.write( "since your problem is in feet we use g = 16<BR>\n" );
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document.write( "1) s(t) = -16t^2 + 20t + 6<BR>\n" );
document.write( "this is the equation of a parabola that curves downward<BR>\n" );
document.write( "the coordinate of a point on the parabola is given by (t, s), that is time t is the x coordinate and height s is the y coordinate,<BR>\n" );
document.write( "we know that the t coordinate of the vertex is given by<BR>\n" );
document.write( "t = -b/(2a) = -20 / (2 *(-16)) = 20/32 = 5/8 = 0.625<BR>\n" );
document.write( "s(0.625) = -16*(0.625)^2 + 20*(0.625) + 6 = 12.25<BR>\n" );
document.write( "maximum height of basketball is 12.25 feet<BR>\n" );
document.write( "here is a graph of the basketball's flight<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-2%2C+5%2C+-2%2C+15%2C+-16x%5E2%2B20x%2B6%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-2%2C+5%2C+-2%2C+15%2C+-16x%5E2%2B20x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "2) height s is 0 when the basketball hits the ground<BR>\n" );
document.write( "-16t^2 +20t +6 = 0<BR>\n" );
document.write( "divide both sides of = by -16<BR>\n" );
document.write( "t^2 -(20/16)t -6/16 = 0<BR>\n" );
document.write( "reduce fractions<BR>\n" );
document.write( "t^2 -(5/4)t -(3/8) = 0<BR>\n" );
document.write( "add 3/8 to both sides of =<BR>\n" );
document.write( "t^2 -(5/4)t = 3/8<BR>\n" );
document.write( "note (1/2) of (5/4) = (5/8)<BR>\n" );
document.write( "t^2 -(5/4)t +(25/64) = (3/8) + (25/64)<BR>\n" );
document.write( "note that 3/8 = 24/64<BR>\n" );
document.write( "(t - 5/8)^2 = 49/64<BR>\n" );
document.write( "take square root of both sides of =<BR>\n" );
document.write( "t - 5/8 = 7/8<BR>\n" );
document.write( "t = 5/8 + 7/8 = 12/8 = 1.5<BR>\n" );
document.write( "after 1.5 seconds the basketball hits the ground<BR>\n" );
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document.write( "compare our answers to 1 and 2 to the graph of the basketball's flight\r<BR>\n" );
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