document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=821922>Question 821922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the maximum value of the equation: y=-16t^2+80t+2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494500 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=494500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given<BR>\n" );
document.write( "(1) -16t^2+80t+2 = 0 which is of the standard quadratic form<BR>\n" );
document.write( "(2) ax^2 + bx + c = 0<BR>\n" );
document.write( "If we set (2) equal to f(x) and let <BR>\n" );
document.write( "(3) y = f(x) we get<BR>\n" );
document.write( "(4) y = ax^2 + bx + c which is also called the formula for a parabola.<BR>\n" );
document.write( "You may have learned that the x-axis of symmetry for the parabola is given by<BR>\n" );
document.write( "(5) x = -b/2a<BR>\n" );
document.write( "In (1) we have a = -16 and b = 80, so we get<BR>\n" );
document.write( "(6) x-axis of symmetry = -(80)/(2*(-16)) or<BR>\n" );
document.write( "(7) x-axis of symmetry = 80/32 or<BR>\n" );
document.write( "(8) x-axis of symmetry = 5/2<BR>\n" );
document.write( "In your problem x = t so we get<BR>\n" );
document.write( "(9) t = 5/2 <BR>\n" );
document.write( "Another property of the parabola is the it has a maximum or minimum when x (or t in this case) is at the x value of the x-axis of symmetry. Therefore set t=5/2 in (1) to get the maximum or<BR>\n" );
document.write( "(10) Max = -16(5/2)^2+80(5/2)+2 or<BR>\n" );
document.write( "(11) Max = -16*25/4 + 80*5/2 + 2 or<BR>\n" );
document.write( "(12) Max = -100 +200 +2 or<BR>\n" );
document.write( "(13) Max = 102<BR>\n" );
document.write( "Answer: The given equation has a maximum value of 102 when t is 5/2.<BR>\n" );
document.write( "PS If you are into calculus, you can get (5) by taking the derivative of (4) with respect to x, set this derivative equal to zero and solve for x, or<BR>\n" );
document.write( "(14) 2*a*x + b = 0 or<BR>\n" );
document.write( "(15) x = -b/2a<BR>\n" );
document.write( "All the derivative is, is the slope of the quadratic, and (15) tells us when the slope is zero, i.e a peak or valley.<BR>\n" );
document.write( " </SPAN>\n" );
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