document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888333>Question 888333</A>: <I><SPAN STYLE=\"word-break: break-all;\">  To obtain maximum strength engineers often design tunnels as parabolic arches. In such a design if the highest point of the arch is 19 m above the road and the road is 20 m wide , determine the equation of the parabolic arch. You may find the equation using any method (vertex form, factored form etc) but you must, <BR>\n" );
document.write( "a) set the bottom left corner of the tunnel as the origin<BR>\n" );
document.write( "b) put your final answer into standard form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537291 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To obtain maximum strength engineers often design tunnels as parabolic arches. In such a design if the highest point of the arch is 19 m above the road and the road is 20 m wide , determine the equation of the parabolic arch. You may find the equation using any method (vertex form, factored form etc) but you must, <BR>\n" );
document.write( "a) set the bottom left corner of the tunnel as the origin<BR>\n" );
document.write( " b) put your final answer into standard form<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Draw the picture.<BR>\n" );
document.write( "You have 3 points at:: (0,0),(20,0),(10,19)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Form: y = ax^2 + bx + c<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Using 0,0 c = 0<BR>\n" );
document.write( "Using 20,0 you get 400a + 20b = 0<BR>\n" );
document.write( "Using 10,19 you get 100a + 10b = 19<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Modify:<BR>\n" );
document.write( "20a + b = 0<BR>\n" );
document.write( "10a + b = 1.9<BR>\n" );
document.write( "----<BR>\n" );
document.write( "10a = -1.9<BR>\n" );
document.write( "a = -0.19<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve for \"b\"::<BR>\n" );
document.write( "10a + b = 1.9<BR>\n" );
document.write( "-1.9 + b = 1.9<BR>\n" );
document.write( "b = 3.8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y = -0.19x^2 + 3.8x<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );