document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165020>Question 165020</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618503080/algebrahomeworkh></A><BR>\n" );
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document.write( "I am having difficulties on how to work this type of word problem. any help appreciated.\r<BR>\n" );
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document.write( "The height s, in feet, of a rock thrown upward at an initial speed of 64ft/sec from a cliff 50 ft. above an ocean beach is given by the function<BR>\n" );
document.write( " s(t) = -16^2 + 64t +50, where t is the time in seconds. Find the maximum height above the beach that the rock will attain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121626 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=121626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ref:<BR>\n" );
document.write( "http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php<BR>\n" );
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document.write( "The quadratic is a parabola:<BR>\n" );
document.write( "f(x) = ax^2 + bx + c<BR>\n" );
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document.write( "If the coefficient 'a' is negative (which is your case), the parabola opens downward (picture -- \"negative\" -- sad face).<BR>\n" );
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document.write( "Therefore, the \"vertex\" of the parabola will give you the \"maximum\".<BR>\n" );
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document.write( "Vertex form of a parabola:<BR>\n" );
document.write( "y= a(x-h)^2+k<BR>\n" );
document.write( "where<BR>\n" );
document.write( "(h, k) is the vertex<BR>\n" );
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document.write( "The idea is to convert your given equation into the \"vertex\" form.<BR>\n" );
document.write( "s(t) = -16t^2 + 64t +50<BR>\n" );
document.write( "Group terms:<BR>\n" );
document.write( "s(t) = (-16^2 + 64t) +50<BR>\n" );
document.write( "s(t) = -16(t^2 - 4t) +50<BR>\n" );
document.write( "\"Complete the square\":<BR>\n" );
document.write( "see:http://www.purplemath.com/modules/sqrquad.htm<BR>\n" );
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document.write( "s(t) = -16(t^2 - 4t + 4) +50 + 4(16)<BR>\n" );
document.write( "s(t) = -16(t^2 - 4t + 4) +50 + 64<BR>\n" );
document.write( "s(t) = -16(t^2 - 4t + 4) + 114<BR>\n" );
document.write( "s(t) = -16(t - 2)^2 + 114<BR>\n" );
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document.write( "Vertex:<BR>\n" );
document.write( "(h,k)= (2,114)<BR>\n" );
document.write( "This says, that at 2 seconds, the rock is at 114 feet.<BR>\n" );
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document.write( "Answer: 114 feet\r<BR>\n" );
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