document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730161>Question 730161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.<BR>\n" );
document.write( "A. What is the initial height (i.e. the height of the building)?<BR>\n" );
document.write( "B. How high did the ball go?<BR>\n" );
document.write( "C. When does the ball hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446516 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=446516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.<BR>\n" );
document.write( "A. What is the initial height (i.e. the height of the building)?<BR>\n" );
document.write( "initial height is when t=0:<BR>\n" );
document.write( "h(t) = -16t^2+48t+32<BR>\n" );
document.write( "h(0) = -16(0)^2+48(0)+32<BR>\n" );
document.write( "h(0) = 32 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "B. How high did the ball go?<BR>\n" );
document.write( "vertex is at max:<BR>\n" );
document.write( "time, at vertex:<BR>\n" );
document.write( "t = -b/(2a)<BR>\n" );
document.write( "t = -48/(2(-16))<BR>\n" );
document.write( "t = -48/(-32)<BR>\n" );
document.write( "t = 3/2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Height at t=3/2:<BR>\n" );
document.write( "h(3/2) = -16(3/2)^2+48(3/2)+32<BR>\n" );
document.write( "h(3/2) = -16(9/4)+24(3)+32<BR>\n" );
document.write( "h(3/2) = -4(9)+24(3)+32<BR>\n" );
document.write( "h(3/2) = -36+72+32<BR>\n" );
document.write( "h(3/2) = 68 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "C. When does the ball hit the ground?<BR>\n" );
document.write( "set h(t) to zero and solve for t:<BR>\n" );
document.write( "h(t) = -16t^2+48t+32<BR>\n" );
document.write( "0 = -16t^2+48t+32<BR>\n" );
document.write( "0 = t^2-3t-2<BR>\n" );
document.write( "solve by applying the \"quadratic formula\" to get:<BR>\n" );
document.write( "t = {3.56, -0.56}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving<BR>\n" );
document.write( "t = 3.56 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic formula follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1x%5E2%2B-3x%2B-2+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-2+=+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=%28-3%29%5E2-4%2A1%2A-2=17 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-2=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=17 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--3%2B-sqrt%28+17+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3%2B-sqrt%28+17+%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-%28-3%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+3.56155281280883 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+3.56155281280883\"   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-%28-3%29-sqrt%28+17+%29%29%2F2%5C1+=+-0.56155281280883 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-3%29-sqrt%28+17+%29%29%2F2%5C1+=+-0.56155281280883\"   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=1x%5E2%2B-3x%2B-2 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-2\"   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=1x%5E2%2B-3x%2B-2+=+1%28x-3.56155281280883%29%2A%28x--0.56155281280883%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-3x%2B-2+=+1%28x-3.56155281280883%29%2A%28x--0.56155281280883%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.56155281280883, -0.56155281280883.\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+1%2Ax%5E2%2B-3%2Ax%2B-2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );