document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207554>Question 1207554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using Desmos calculator design a roller coaster.\r<BR>\n" );
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document.write( "• use only quadratic functions<BR>\n" );
document.write( "• create one full loop<BR>\n" );
document.write( "• start and end your roller coaster slightly a above the ground level (x-axes will<BR>\n" );
document.write( "indicate the ground level)<BR>\n" );
document.write( "• make at least one \"function\" below the ground level </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847943 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To create a roller coaster on Desmos using only quadratic functions, we'll need to piece together multiple functions, each defining a specific section of the track. Here's a basic outline:\r<BR>\n" );
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document.write( "Initial Climb: A quadratic function that starts at ground level and rises to a peak.<BR>\n" );
document.write( "First Drop: A quadratic function that descends from the peak, going below ground level.<BR>\n" );
document.write( "Loop: Two quadratic functions, one for the upward part of the loop and one for the downward part.<BR>\n" );
document.write( "Final Drop and Leveling Off: A quadratic function that descends from the loop and levels off slightly above ground level.<BR>\n" );
document.write( "Here's a possible set of equations:\r<BR>\n" );
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document.write( "f(x) = -0.05(x-10)^2 + 10  // Initial climb<BR>\n" );
document.write( "g(x) = -0.1(x-20)^2 + 15  // First drop<BR>\n" );
document.write( "h(x) = 0.05(x-30)^2 - 5  // Upward part of the loop<BR>\n" );
document.write( "i(x) = -0.05(x-40)^2 + 5  // Downward part of the loop<BR>\n" );
document.write( "j(x) = -0.02(x-50)^2 + 1  // Final drop and leveling off<BR>\n" );
document.write( "To input these functions into Desmos:\r<BR>\n" );
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document.write( "Go to https://www.desmos.com/calculator<BR>\n" );
document.write( "In the expression bar, type each function one by one, pressing Enter after each.<BR>\n" );
document.write( "You can adjust the coefficients to fine-tune the shape of the roller coaster. For example, increasing the coefficient of the squared term will make the curve steeper, while decreasing it will make it flatter.\r<BR>\n" );
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document.write( "Remember to experiment and have fun! You can create more complex roller coasters by adding more functions and adjusting the parameters.\r<BR>\n" );
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document.write( "Tip: To visualize the roller coaster better, you can adjust the viewing window in Desmos. Click on the wrench icon in the top right corner and adjust the x-min, x-max, y-min, and y-max values. </SPAN>\n" );
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