document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874241>Question 874241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f(t) =-5t2 + 20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? <BR>\n" );
document.write( "So that's the question and I am totally lost. Would you mind explaining? *I am reviewing out a textbook, I am trying to get help our teacher said it was fine to ask people how to do it if your not understanding. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527392 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plug in f(t) = 0. We do this because f(t) represents the height and a height of 0 means you're at the ground.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(t) =-5t^2 + 20t + 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 = -5t^2 + 20t + 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5t^2 + 20t + 60 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now solve for t using the quadratic formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for t:<BR><BR>\n" );
document.write( "\n" );
document.write( "  <BR>\n" );
document.write( "  Starting with the general quadratic<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  the general solution using the quadratic equation is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2At%5E2%2B20%2At%2B60=0 ALIGN=MIDDLE  ALT=\"-5%2At%5E2%2B20%2At%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-5 ALIGN=MIDDLE  ALT=\"a=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=20 ALIGN=MIDDLE  ALT=\"b=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=60 ALIGN=MIDDLE  ALT=\"c=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-5%2A60+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-5%2A60+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-5, b=20, and c=60<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400-4%2A-5%2A60+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400-4%2A-5%2A60+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 20 to get 400  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400%2B1200+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400%2B1200+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A60%2A-5 ALIGN=MIDDLE  ALT=\"-4%2A60%2A-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200 ALIGN=MIDDLE  ALT=\"1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+1600+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+1600+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+40%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+40%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+40%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+40%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -5 to get -10<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So now the expression breaks down into two parts<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B+40%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B+40%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+-+40%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+-+40%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Lets look at the first part:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-20+%2B+40%29%2F-10 ALIGN=MIDDLE  ALT=\"x=%28-20+%2B+40%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=20%2F-10 ALIGN=MIDDLE  ALT=\"t=20%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2 ALIGN=MIDDLE  ALT=\"t=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So one answer is<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2 ALIGN=MIDDLE  ALT=\"t=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets look at the second part:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-20+-+40%29%2F-10 ALIGN=MIDDLE  ALT=\"x=%28-20+-+40%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-60%2F-10 ALIGN=MIDDLE  ALT=\"t=-60%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So another answer is<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So our solutions are:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2 ALIGN=MIDDLE  ALT=\"t=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Ignore the negative t value (negative time values make no sense)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The only practical solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+6 ALIGN=MIDDLE  ALT=\"t+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So it takes 6 seconds for the object to hit the ground. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );