document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185467>Question 1185467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this function notation word problem!<BR>\n" );
document.write( "\"Use function notation to rewrite the following phrases below.<BR>\n" );
document.write( "A ball is thrown straight up with a certain speed, then its height above the ground (measured in meters) after t seconds is given by the following equation:\r<BR>\n" );
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document.write( "h(t) = −4.9t2+30t\r<BR>\n" );
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document.write( "1. The height of the ball 1 second after being thrown<BR>\n" );
document.write( "2. The height of the ball 2 seconds after being thrown<BR>\n" );
document.write( "3. The height of the ball t seconds after being thrown<BR>\n" );
document.write( "4. The change in height of the ball between 1 and 2 seconds<BR>\n" );
document.write( "5. The change in height of the ball between 1.5 and 2.5 seconds<BR>\n" );
document.write( "6. The change in height of the ball between a and b seconds\"<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 #816294 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the function is:\r<BR>\n" );
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document.write( "h(t) = -4.9 * t^2 + 30*t\r<BR>\n" );
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document.write( "t^2 means t raised to the second power.\r<BR>\n" );
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document.write( "answers to your questions are shown below:\r<BR>\n" );
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document.write( "1. The height of the ball 1 second after being thrown\r<BR>\n" );
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document.write( "h(1) = -4.9 * 1^2 + 30*1 = 25.1 meters\r<BR>\n" );
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document.write( "2. The height of the ball 2 seconds after being thrown\r<BR>\n" );
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document.write( "h(2) = -4.9 * 2^2 + 30 * 2 = 40.5 meters\r<BR>\n" );
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document.write( "3. The height of the ball t seconds after being thrown\r<BR>\n" );
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document.write( "h(t) = -4.9 * t^2 + 30 * t\r<BR>\n" );
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document.write( "4. The change in height of the ball between 1 and 2 seconds\r<BR>\n" );
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document.write( "h(2) - h(1) = -4.9 * 2^2 + 30 * 2 - (-4.9 * 1^2 + 30 * 1) = 15.3 meters\r<BR>\n" );
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document.write( "5. The change in height of the ball between 1.5 and 2.5 seconds\r<BR>\n" );
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document.write( "h(2.5) - h(1.5) = -4.9 * 2.5^2 + 30 * 2.5 - (-4.9 * 1.5^2 + 30 * 1.5) = 10.4 meters\r<BR>\n" );
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document.write( "6. The change in height of the ball between a and b seconds\"\r<BR>\n" );
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document.write( "h(b) - h(a) = -4.9 * b^2 + 30 * b - (-4.9 * a^2 + 30 * a) equals:<BR>\n" );
document.write( "-4.9 * b^2 + 30 * b + 4.9 * a^2 - 30 * a  ***** 1<BR>\n" );
document.write( "you can reorder the terms in descending order of degree as shown below:<BR>\n" );
document.write( "-4.9 * b^2 + 4.9 * a^2 + 30 * b - 30 * a.  ***** 1<BR>\n" );
document.write( "you can factor the terms as shown below:<BR>\n" );
document.write( "factor out the -4.9 and factor out the 30 to get:<BR>\n" );
document.write( "-4.9 * (b^2 - a^2) + 30 * (b - a) ***** 1\r<BR>\n" );
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document.write( "***** 1<BR>\n" );
document.write( "you can use either version and you should be ok.\r<BR>\n" );
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document.write( "the factored version should be equivalent to the unfactored version.<BR>\n" );
document.write( "you can check to see if this is good by using one of the previous problems.<BR>\n" );
document.write( "for example: <BR>\n" );
document.write( "h(2.5) - h(1.5) becomes:<BR>\n" );
document.write( "4.9 * (-(2.5^2 + 1.5^2) + 30 * (2.5 - 1.5) which becomes:<BR>\n" );
document.write( "-4.9 * 4 + 30 which iw equal to 10.4.\r<BR>\n" );
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document.write( "this confirms the factoring was good.<BR>\n" );
document.write( "if you try to do this yourself, be careful of the minus signs.<BR>\n" );
document.write( "they can mess up your calculations.<BR>\n" );
document.write( "i had to do it a couple of time before i got it right.\r<BR>\n" );
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