document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=390339>Question 390339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides.<BR>\n" );
document.write( "a) Find the equation of the parabola (Assume that the origin is at the center of the road) - Show all work<BR>\n" );
document.write( "b) How far from the center of the road is the road surface 0.1 foot lower than in the middle? -show all work.\r<BR>\n" );
document.write( "\n" );
document.write( "please show work and thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276859 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=276859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A road is 32 feet wide is 0.4 foot higher in the center then it is on its sides.<BR>\n" );
document.write( "a) Find the equation of the parabola (Assume that the origin is at the center of the road)<BR>\n" );
document.write( "Using ax^2 + bx + c = y<BR>\n" );
document.write( "Since the center is at origin, (x=0) then c = +.4<BR>\n" );
document.write( "x=-16; y=0<BR>\n" );
document.write( "-16^2a - 16b + .4 = 0<BR>\n" );
document.write( "256a - 16b = -.4<BR>\n" );
document.write( "x=16; y=0<BR>\n" );
document.write( "16^2a + 16b + .4 = 0<BR>\n" );
document.write( "256a + 16b = -.4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "add these two equations<BR>\n" );
document.write( "256a - 16b = -.4<BR>\n" );
document.write( "256a + 16b = -.4<BR>\n" );
document.write( "-------------------adding eliminates b<BR>\n" );
document.write( "512a = -.8<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.8%29%2F512 ALIGN=MIDDLE  ALT=\"%28-.8%29%2F512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.0015625<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b, it will equal 0, as you can see<BR>\n" );
document.write( "-.0001562(256) + 16b = -.4<BR>\n" );
document.write( "-.4 + 16b = -.4<BR>\n" );
document.write( "16b = -.4 + .4<BR>\n" );
document.write( "16b = 0<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "Therefore:<BR>\n" );
document.write( "The equation: -.0015625x^2 + .4 = y<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) How far from the center of the road is the road surface 0.1 foot lower than in the middle?<BR>\n" );
document.write( "y = .3<BR>\n" );
document.write( "-.0015625x^2 + .4 = .3<BR>\n" );
document.write( "-.0015625x^2 = .3 - .4<BR>\n" );
document.write( "-.0015625x^2 = -.1<BR>\n" );
document.write( "x^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.1%29%2F%28-.0015625%29 ALIGN=MIDDLE  ALT=\"%28-.1%29%2F%28-.0015625%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x^2 = 64<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 8 ft from the center it is .1 ft lower than the middle </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );