document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1760>Question 1760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to come up with the general equation of a quadratic function for the following word problem. Can you help me get started please?\r<BR>\n" );
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document.write( "A large awning is being designed for a hotel entrance and drive.  The roof is to be a section of a parabola, with the vertex attached to the hotel wall 16 feet abve the ground, and supported by 10 foot wall posts that are 12 feet away from the hotel wall.<BR>\n" );
document.write( "Come up with a general eqaution of a quadratic function that would model the roof of the awning.\r<BR>\n" );
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document.write( "Thanks for ANY help.  I'm completely stuck on how to go about this problem algebraically.\r<BR>\n" );
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document.write( "Noelle<BR>\n" );
document.write( "marknoni@comcast.net </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to start with this...draw a picture. Draw a vertical line for the wall and a floor line. Draw a rough curve from the wall arcing down and mark on the height 16 feet, the pole, 10 feet and te distance from the wall, 12 feet.\r<BR>\n" );
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document.write( "The leap of faith you need is to visualise this as a graph. Extend the wall up and call this the y-axis. Where the awning touches the wall, draw a horizontal line for the x-axis. Now carry on the awning curve to the other lower quadrant of your graph, so you have a classic parabola shape.\r<BR>\n" );
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document.write( "What you know is the following:\r<BR>\n" );
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document.write( "1. the curve passes through the origin of these axes (0,0).<BR>\n" );
document.write( "2. the curve passes through 2 other points that we know...namely (12, -6) and (-12,6). Have a think about these and see if you can see where these numbers come from. They are the points where the awning touches the top of the pole.\r<BR>\n" );
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document.write( "Now, we just have to fit this 2 bits of info to the general equation of a parabola... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To do this, we put the info we know into the general equation...First, we know that x=0 when y=0. This gives us that c must be zero. Therefore our equation is now of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I shall leave you to do the rest :-)\r<BR>\n" );
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document.write( "Note, the curve is an \"upside down parabola\" so you should get a to be a negative number.\r<BR>\n" );
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document.write( "Jon\r<BR>\n" );
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