document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066494>Question 1066494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket was launched from a platform. The function h(t)=16t-5t^2+3 expresses the height in feet of the rocket over time in seconds. Find the average rate of change over the interval (0,2). State the domain and range.\r<BR>\n" );
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document.write( "I am having problems finding the Domain.\r<BR>\n" );
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document.write( "Average rate of change is: 15-3/2-0 = 6ft/sec<BR>\n" );
document.write( "Range is: x=-16/2(-5) = 1.6  <BR>\n" );
document.write( "  x=16(1.6)-5(103)^2+3<BR>\n" );
document.write( "  R={0,15.5}\r<BR>\n" );
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document.write( "Please help me find the Domain.<BR>\n" );
document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681684 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=681684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Average rate of change for a function f over an interval [a, b] is<BR>\n" );
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document.write( "(f(b) - f(a)) / (b - a) <BR>\n" );
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document.write( "We are given the following function h and the interval (0, 2)<BR>\n" );
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document.write( "Note average rate of change is usually stated for CLOSED intervals<BR>\n" );
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document.write( "h(t) = -5t^2 +16t +3<BR>\n" );
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document.write( "h(0) = -5(0)^2 +16(0) +3 = 3<BR>\n" );
document.write( "h(2) = -5(2)^2 +16(2) +3 = 15<BR>\n" );
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document.write( "Average rate of change = (15 - 3) / (2 - 0) = 6 feet per second<BR>\n" );
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document.write( "Domain is (0, 2)<BR>\n" );
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document.write( "We need to find coordinates for the Vertex of h(t)<BR>\n" );
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document.write( "t = -16 / -10 = 8/5 = 1.6<BR>\n" );
document.write( "h(1.6) = -5(1.6)^2 +16(1.6) +3 = 15.8<BR>\n" );
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document.write( "This tells us that the max value(15.8) for h(t) occurs at t = 1.6<BR>\n" );
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document.write( "Range is (3, 15.8]<BR>\n" );
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document.write( "h(t) is a parabola that curves downward, here is its graph<BR>\n" );
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