document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=889534>Question 889534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bridge is to be built across a waterway which is<BR>\n" );
document.write( "50 feet wide and is frequented by ships. The bridge design team determines that a parabolic<BR>\n" );
document.write( "opening underneath the bridge is the best possible option for both structure and functionality<BR>\n" );
document.write( "(keeping the waterway passable by ships while still being safe for vehicles to travel across).<BR>\n" );
document.write( "If parabolic opening touches the ground right at the edges of the waterway and the maximum<BR>\n" );
document.write( "height of the opening is 60ft, what is the maximum height that a 20-foot wide boat could be<BR>\n" );
document.write( "and still pass through the opening? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538236 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=538236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bridge is to be built across a waterway which is<BR>\n" );
document.write( "50 feet wide and is frequented by ships. The bridge design team determines that a parabolic<BR>\n" );
document.write( "opening underneath the bridge is the best possible option for both structure and functionality<BR>\n" );
document.write( "(keeping the waterway passable by ships while still being safe for vehicles to travel across).<BR>\n" );
document.write( "If parabolic opening touches the ground right at the edges of the waterway and the maximum<BR>\n" );
document.write( "height of the opening is 60ft, what is the maximum height that a 20-foot wide boat could be<BR>\n" );
document.write( "and still pass through the opening?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y<BR>\n" );
document.write( "have the axis of symmetry at the origin, then c = 60<BR>\n" );
document.write( "x intercepts occur at x = -25 and x = +25<BR>\n" );
document.write( "Two equations<BR>\n" );
document.write( "-25^2(a) -25b + 60 = 0<BR>\n" );
document.write( "625a - 25b + 60 = 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "+25^2(a) + 25b + 60 = 0<BR>\n" );
document.write( "625a + 25b + 60 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination, add the two equations<BR>\n" );
document.write( "625a - 25b + 60 = 0<BR>\n" );
document.write( "625a + 25b + 60 = 0<BR>\n" );
document.write( "-------------------- adding eliminates b find a<BR>\n" );
document.write( "1250a + 120 = 0<BR>\n" );
document.write( "1250a = - 120<BR>\n" );
document.write( "a = -120/1250<BR>\n" );
document.write( "a = -.096<BR>\n" );
document.write( "The equation<BR>\n" );
document.write( "y = -.096x^2 + 60<BR>\n" );
document.write( "looks like this <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+50%2C+-20%2C+80%2C+-.096x%5E2%2B60%2C+50%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+50%2C+-20%2C+80%2C+-.096x%5E2%2B60%2C+50%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "20' wide boat can be represented by the distance between -10 and +10<BR>\n" );
document.write( "Find the height at these points<BR>\n" );
document.write( "y = -.096(10^2) + 60<BR>\n" );
document.write( "y = -.9.6 + 60<BR>\n" );
document.write( "y = 50.4 ft<BR>\n" );
document.write( "a 50 ft high boat would just be able pass through (green line)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );