document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426962>Question 426962</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Kayli wants to build a parabolic bridge over a stream in her backyard. The <BR>\n" );
document.write( "bridge must span a width of 200 cm. It must be at least 51 cm high where it is <BR>\n" );
document.write( "30 cm from the bank on each side. How high will her bridge be?\r<BR>\n" );
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document.write( "I have tried many ways of figuring this question out. However, I was <BR>\n" );
document.write( "unsuccessful. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296928 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=296928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Kayli wants to build a parabolic bridge over a stream in her backyard. The<BR>\n" );
document.write( "bridge must span a width of 200 cm. It must be at least 51 cm high where it is<BR>\n" );
document.write( "30 cm from the bank on each side. How high will her bridge be?<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Start by placing the origin of the (x,y) coordinate system at the left bank of the 200 cm span. We now have 3 points of the parabola to work with, the origin,(0,0), 30 cm from the bank,(30,51) and the vertex,(100,k),k(height of bridge) to be determined.Standard form of a parabola: y=A(x-h)^2+k where (h,k) are the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Solving for A with two equations:<BR>\n" );
document.write( "Using point (30,51)<BR>\n" );
document.write( "51=A(30-100)^2+k<BR>\n" );
document.write( "Using origin (0,0)<BR>\n" );
document.write( "0=A(0-100)^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "51=A(70)^2+k<BR>\n" );
document.write( " 0=A(100)^2+k<BR>\n" );
document.write( "51=A(4900)+k<BR>\n" );
document.write( " 0=A(10000)+k<BR>\n" );
document.write( "subtract algebraically<BR>\n" );
document.write( "51=A(4900-10000)+0<BR>\n" );
document.write( "51=A(-5100)<BR>\n" );
document.write( "A=51/-5100=-1/100<BR>\n" );
document.write( "solving for k<BR>\n" );
document.write( "y=-1/100(x-100)^2+k<BR>\n" );
document.write( "51=-1/100(30-100)^2+k<BR>\n" );
document.write( "51=-49+k<BR>\n" );
document.write( "k=100 cm <BR>\n" );
document.write( "ans:height of parabolic bridge=100cm<BR>\n" );
document.write( "See graph of parabola below:<BR>\n" );
document.write( "y=-(1/100)(x-100)^2+100<BR>\n" );
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