document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184046>Question 184046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The arch of a bridge is in the shape of a parabola and is 14ft high at the center and 20ft wide at the base.\r<BR>\n" );
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document.write( "a.) What is the tallest 8ft wide truck that can pass through the arch?\r<BR>\n" );
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document.write( "b.) what is the widest 12ft high truck that can pass through the arch? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138168 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would plot the parabola and put one x-intercept at the origin<BR>\n" );
document.write( "(0,0) and the other x-intercept at (20,0). That would put the <BR>\n" );
document.write( "y-intercept at the origin.<BR>\n" );
document.write( "The general equation is<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "I have to find a, b, and c<BR>\n" );
document.write( "since one intercept is at (0,0), I can say<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a%2A0%5E2+%2B+b%2A0+%2B+c ALIGN=MIDDLE  ALT=\"0+=+a%2A0%5E2+%2B+b%2A0+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+0 ALIGN=MIDDLE  ALT=\"c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And the other x-intercept is at (20,0)<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a%2A20%5E2+%2B+b%2A20 ALIGN=MIDDLE  ALT=\"0+=+a%2A20%5E2+%2B+b%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400a+=+-20b ALIGN=MIDDLE  ALT=\"400a+=+-20b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20a ALIGN=MIDDLE  ALT=\"b+=+-20a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The arch is 14 ft high at the center<BR>\n" );
document.write( "This is the vertex. The x-value of the vertex is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F%282a%29+=+%28-%28-20a%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b%29%2F%282a%29+=+%28-%28-20a%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b%29%2F%282a%29+=+10 ALIGN=MIDDLE  ALT=\"+%28-b%29%2F%282a%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the x-coordinate of the vertex<BR>\n" );
document.write( "The problem says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+14 ALIGN=MIDDLE  ALT=\"y+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the vertex<BR>\n" );
document.write( "so, (10,14) is a point on the curve<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+=+a%2A10%5E2+%2B+b%2A10+ ALIGN=MIDDLE  ALT=\"14+=+a%2A10%5E2+%2B+b%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From above, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20a ALIGN=MIDDLE  ALT=\"b+=+-20a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+=+100a+-+200a ALIGN=MIDDLE  ALT=\"14+=+100a+-+200a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100a+=+14 ALIGN=MIDDLE  ALT=\"-100a+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-+.14 ALIGN=MIDDLE  ALT=\"a+=+-+.14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20a ALIGN=MIDDLE  ALT=\"b+=+-20a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20%2A%28-.14%29 ALIGN=MIDDLE  ALT=\"b+=+-20%2A%28-.14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2.8 ALIGN=MIDDLE  ALT=\"b+=+2.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-.14x%5E2+%2B+2.8x ALIGN=MIDDLE  ALT=\"y+=+-.14x%5E2+%2B+2.8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll plot it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-2%2C+25%2C+-2%2C+16%2C+-.14x%5E2+%2B+2.8x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-2%2C+25%2C+-2%2C+16%2C+-.14x%5E2+%2B+2.8x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "a.) What is the tallest 8ft wide truck that can pass through the arch?<BR>\n" );
document.write( "If it goes straight down the middle, it will cover 4 ft on either side<BR>\n" );
document.write( "The center of the arch is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. 4 on either side would<BR>\n" );
document.write( "be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+14 ALIGN=MIDDLE  ALT=\"x+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I should get the same y-value<BR>\n" );
document.write( "for both of these<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-.14x%5E2+%2B+2.8x ALIGN=MIDDLE  ALT=\"y+=+-.14x%5E2+%2B+2.8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-.14%2A6%5E2+%2B+2.8%2A6 ALIGN=MIDDLE  ALT=\"y+=+-.14%2A6%5E2+%2B+2.8%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5.04+%2B+16.8 ALIGN=MIDDLE  ALT=\"y+=+-5.04+%2B+16.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+11.76 ALIGN=MIDDLE  ALT=\"y+=+11.76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tallest truck is 11.76 ft tall<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "b.) what is the widest 12ft high truck that can pass through the arch?<BR>\n" );
document.write( "It is 6 ft on either side of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+16 ALIGN=MIDDLE  ALT=\"x+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can use either one to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-.14x%5E2+%2B+2.8x ALIGN=MIDDLE  ALT=\"y+=+-.14x%5E2+%2B+2.8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-.14%2A16%5E2+%2B+2.8%2A16 ALIGN=MIDDLE  ALT=\"y+=+-.14%2A16%5E2+%2B+2.8%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-35.84+%2B+44.8 ALIGN=MIDDLE  ALT=\"y+=+-35.84+%2B+44.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8.96 ALIGN=MIDDLE  ALT=\"y+=+8.96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tallest truck is 8.96 ft tall </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );