document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831087>Question 831087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #1. <BR>\n" );
document.write( "A person standing close to the edge on the top of a 122-foot building throws a baseball vertically upward. The quadratic equation\r<BR>\n" );
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document.write( " h = -16 t^2 + 96 t + 122\r<BR>\n" );
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document.write( "models the ball's height  h   above the ground in feet, t seconds after it was thrown.\r<BR>\n" );
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document.write( "How high is the ball after 3 seconds?\r<BR>\n" );
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document.write( "How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501150 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=501150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1. <BR>\n" );
document.write( "A person standing close to the edge on the top of a 122-foot building throws a baseball vertically upward. The quadratic equation\r<BR>\n" );
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document.write( " h = -16 t^2 + 96 t + 122\r<BR>\n" );
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document.write( "models the ball's height  h   above the ground in feet, t seconds after it was thrown.\r<BR>\n" );
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document.write( "How high is the ball after 3 seconds?<BR>\n" );
document.write( "set t=3 and solve:<BR>\n" );
document.write( "h = -16*3^2 + 96*3 + 122<BR>\n" );
document.write( "h = -16*9 + 96*3 + 122<BR>\n" );
document.write( "h = -144 + 288 + 122<BR>\n" );
document.write( "h = 144 + 122<BR>\n" );
document.write( "h = 266 feet\r<BR>\n" );
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document.write( "How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.<BR>\n" );
document.write( "set h=0 and solve for t:<BR>\n" );
document.write( "0 = -16t^2 + 96 t + 122<BR>\n" );
document.write( "solve using the quadratic formula to get:<BR>\n" );
document.write( "t={-1.1, 7.1}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving:<BR>\n" );
document.write( "t = 7.1 seconds<BR>\n" );
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document.write( "Details of quadratic formula:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B96x%2B122+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B96x%2B122+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2896%29%5E2-4%2A-16%2A122=17024 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2896%29%5E2-4%2A-16%2A122=17024\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=17024 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-96%2B-sqrt%28+17024+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-96%2B-sqrt%28+17024+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2896%29%2Bsqrt%28+17024+%29%29%2F2%5C-16+=+-1.07737660757502 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2896%29%2Bsqrt%28+17024+%29%29%2F2%5C-16+=+-1.07737660757502\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2896%29-sqrt%28+17024+%29%29%2F2%5C-16+=+7.07737660757502 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2896%29-sqrt%28+17024+%29%29%2F2%5C-16+=+7.07737660757502\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B96x%2B122 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B96x%2B122\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B96x%2B122+=+-16%28x--1.07737660757502%29%2A%28x-7.07737660757502%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B96x%2B122+=+-16%28x--1.07737660757502%29%2A%28x-7.07737660757502%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.07737660757502, 7.07737660757502.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B96%2Ax%2B122+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B96%2Ax%2B122+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );