document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366328>Question 366328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Owachomo Natural Bridge is found in National Bridges Natural Monument in Utah. If the origin is located at one end of the natural arch, the curve can be modeled by the equation h=-0.043d^2+2.365d where h meters is the height of the arch, and d meters is the horizontal distance from the origin.<BR>\n" );
document.write( "a) what is the maximum height of the arch, to the nearest hundredth of a meter?<BR>\n" );
document.write( "b) What is the width of the arch at the base?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #261064 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=261064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> anytime you have a quadratic equation such as the one you pose<BR>\n" );
document.write( "there are several ways to answer your question.<BR>\n" );
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document.write( "1) complete the square<BR>\n" );
document.write( "h=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.043d%5E2%2B2.363d=-0.043%28d%5E2-55d%2B%2855%2F2%29%5E2-%2855%2F2%29%5E2%29=-0.043%28d-55%2F2%29%5E2%2B32.51 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the maximum height is 32.51 meters when d=55/2=27.5 meters<BR>\n" );
document.write( "==<BR>\n" );
document.write( "Another way to figure this out is to remember that a quadratic equation ofthe form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > has its vertex at x=-b/(2a) and that the vertex (minimum if a>0 or maximum if a<0) is found by substituting x=-b/(2a) back into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "--<BR>\n" );
document.write( "so in your equation a=-0.043 and b=2.363<BR>\n" );
document.write( "since a<0 the vertex is a maximum and its found at x=-2.363/(2*(-0.043))=27.5<BR>\n" );
document.write( "so substitute x=27.5 in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.043x%5E2%2B2.363x ALIGN=MIDDLE  ALT=\"y=-0.043x%5E2%2B2.363x\"   DISABLED_style= \"max-width:90%; height:auto;\" > yielding<BR>\n" );
document.write( "y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.043%2A27.5%5E2%2B2.363%2A27.5 ALIGN=MIDDLE  ALT=\"-0.043%2A27.5%5E2%2B2.363%2A27.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=32.46 <BR>\n" );
document.write( "--<BR>\n" );
document.write( "some rounding error between this method and the previous method, otherwise the same answer.<BR>\n" );
document.write( "  <BR>\n" );
document.write( " </SPAN>\n" );
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