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 #537292 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=537292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Working from standard form will be easier.\r<BR>\n" );
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document.write( "The road being 20 m wide means that half-way from the origin  is  10 m, the \"x\" value for the vertex.  The y value for the highest point is 19 m.  The vertex is therefore (10,19).\r<BR>\n" );
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document.write( "Equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-10%29%5E2%2B19 ALIGN=MIDDLE  ALT=\"y=a%28x-10%29%5E2%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You also are given as instruced in part (a) that (0,0) is one of the points.  This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%280-10%29%5E2%2B19 ALIGN=MIDDLE  ALT=\"0=a%280-10%29%5E2%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100a=-19 ALIGN=MIDDLE  ALT=\"100a=-19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-%2819%2F100%29 ALIGN=MIDDLE  ALT=\"a=-%2819%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The equation fully in standard form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%2819%2F100%29%28x-10%29%5E2%2B19%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%2819%2F100%29%28x-10%29%5E2%2B19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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