document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181301>Question 1181301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a person standing on the edge of a cliff throws a rock in the air. the path of the rock is described by the function: h(t)= -2t^2 +8t + 6, 2) where h(t) is the height in meters, above the ground and t us the time in seconds.\r<BR>\n" );
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document.write( "a) what height was the rock thrown into the air<BR>\n" );
document.write( "b) determine the vertex of then function by completing the square<BR>\n" );
document.write( "c) at what time does the rock reach its optimal height<BR>\n" );
document.write( "d) does this this function have a maximum or minimum value? how do you know? state the max/min<BR>\n" );
document.write( "e) state the rang of the function as it applies to the real-life model of the situation described. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811220 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h(t)=-2t^2+8t+6.2.<BR>\n" );
document.write( "a) This is the constant 6.2 m<BR>\n" );
document.write( "b)-2t^2+8t+6.2=h(t)<BR>\n" );
document.write( "-2(t^2-4t)+6.2=h(t)<BR>\n" );
document.write( "complete the square by taking half of -4 and squaring it, then adding 8 to the constant to balance the equation.<BR>\n" );
document.write( "-2(t^2-4t+4)+14.2<BR>\n" );
document.write( "-2(t-2)^2+14.2<BR>\n" );
document.write( "The vertex is at (2, 14.2), changing the sign of h and keeping the same sign of k.<BR>\n" );
document.write( "This is 2 seconds and 14.2 m<BR>\n" );
document.write( "c) Not sure what optimal height means in the context of this question but 14.2 m is maximum height<BR>\n" );
document.write( "d)Maximum value given the negative quadratic, and that is 14.2 m after 2 seconds<BR>\n" );
document.write( "e) The range needs the time it takes to hit or be 0.<BR>\n" );
document.write( "so-2t^2+8t+6.2=0<BR>\n" );
document.write( "ad t^2-4t-3.1=0, dividing by -2<BR>\n" );
document.write( "t=(1/2)(4+/- sqrt (16+12.4)) and sqrt (28.4)=5.33<BR>\n" );
document.write( "positive root is 4.66 m. The range of the function is [0, 4.66] units seconds<BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C6%2C-5%2C20%2C-2x%5E2%2B8x%2B6.2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C6%2C-5%2C20%2C-2x%5E2%2B8x%2B6.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Can check this by vertex = -b/2a which is -8/-4 or 2 seconds<BR>\n" );
document.write( "h(2)=-8+16+6.2=14.2<BR>\n" );
document.write( "Note: the graph is plotting height with time, not distance with time.<BR>\n" );
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