document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205704>Question 205704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry this is a really long problem and I am completely stumped about how to start and what to do.\r<BR>\n" );
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document.write( "Chuck is standing atop a high platform and fires a rock up into the air with his slingshot. While it is in flight, the rock's distance about the ground is a quadratic function of time. 1 second after firing it, the rock is 68 meters high, at 2 seconds it's 96 meters, and at 3 seconds it's 114 meters above ground. Use this information to answer the following questions.\r<BR>\n" );
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document.write( "a. Find and write the quadratic equation for the function<BR>\n" );
document.write( "b. What is the highest point the rock will be above ground?<BR>\n" );
document.write( "c. How high is the platform from which Chuck fires the rock? (Hint: Time = 0)<BR>\n" );
document.write( "d. When will the rock hit the ground?<BR>\n" );
document.write( "e. On its way down, instead of hitting the ground, the rock goes into a nearly empty well. It splashes into the water (hits bottom) exactly 10 seconds after Chuck fired it. How deep is the well?\r<BR>\n" );
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document.write( "Like I said really long and really confusing for me. Any help is really appreciated </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155341 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=155341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Chuck is standing atop a high platform and fires a rock up into the air with his slingshot. While it is in flight, the rock's distance about the ground is a quadratic function of time. 1 second after firing it, the rock is 68 meters high, at 2 seconds it's 96 meters, and at 3 seconds it's 114 meters above ground. Use this information to answer the following questions.<BR>\n" );
document.write( "a. Find and write the quadratic equation for the function<BR>\n" );
document.write( "Because a \"quadratic equation\" is:<BR>\n" );
document.write( "f(t) = at^2 + bt + c<BR>\n" );
document.write( "We have three unknowns: a, b, and c<BR>\n" );
document.write( "Therefore, we need three equations.  We get this from:<BR>\n" );
document.write( "1 second after firing it, the rock is 68 meters high, <BR>\n" );
document.write( "at 2 seconds it's 96 meters, and <BR>\n" );
document.write( "at 3 seconds it's 114 meters above ground.<BR>\n" );
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document.write( "Our three equations are:<BR>\n" );
document.write( "68 = a(1)^2 + b(1) + c<BR>\n" );
document.write( "96 = a(2)^2 + b(2) + c<BR>\n" );
document.write( "114 = a(3)^2 + b(3) + c<BR>\n" );
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document.write( "Or, rewritten:<BR>\n" );
document.write( "68 = a + b + c<BR>\n" );
document.write( "96 = 4a + 2b + c<BR>\n" );
document.write( "114 = 9a + 3b + c<BR>\n" );
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document.write( "Solve the above system of equations to find a, b and c.  Then put it back into:<BR>\n" );
document.write( "f(t) = at^2 + bt + c<BR>\n" );
document.write( "This will be your \"quadratic equation\" describing the the height (meters) based on time (sec).  <BR>\n" );
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document.write( "b. What is the highest point the rock will be above ground?<BR>\n" );
document.write( "find the vertex of the quadratic found in parta<BR>\n" );
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document.write( "c. How high is the platform from which Chuck fires the rock? (Hint: Time = 0)<BR>\n" );
document.write( "Set t=0 and solve.  It will be 'c'.<BR>\n" );
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document.write( "d. When will the rock hit the ground?<BR>\n" );
document.write( "Set f(x)=0 and solve for t<BR>\n" );
document.write( "0 = at^2 + bt + c<BR>\n" );
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document.write( "e. On its way down, instead of hitting the ground, the rock goes into a nearly empty well. It splashes into the water (hits bottom) exactly 10 seconds after Chuck fired it. How deep is the well? <BR>\n" );
document.write( "Add 10 the answer from part d and plug it into your quadratic equation to find f(x), it will be a negative number (because it is below the ground).  The absolute value will be the depth of the well.\r<BR>\n" );
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document.write( "Write back if you get stuck. </SPAN>\n" );
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