document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013457>Question 1013457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a parabolic arch has a width of 18 m across the bottom. at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629815 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=629815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  a parabolic arch has a width of 18 m across the bottom.<BR>\n" );
document.write( " at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?<BR>\n" );
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document.write( "Using the form ax^2 + bx + c = y<BR>\n" );
document.write( "arch will be going thru origin, 0,0 so c = 0<BR>\n" );
document.write( "Using two pairs; x=3; y=3 and x=15, y=3, construct two equations<BR>\n" );
document.write( "x=3; y=3<BR>\n" );
document.write( "9a + 3b = 3<BR>\n" );
document.write( "Simplify,divide by 3<BR>\n" );
document.write( "3a + b = 1<BR>\n" );
document.write( "b = (-3a+1)<BR>\n" );
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document.write( "x=15; y=3<BR>\n" );
document.write( "225a + 15b = 3<BR>\n" );
document.write( "simplify, divide b 3<BR>\n" );
document.write( " 75a + 5b = 1<BR>\n" );
document.write( "Replace b with (-3a+1)<BR>\n" );
document.write( "75a + 5(-3a+1) = 1<BR>\n" );
document.write( "75a - 15a + 5 = 1<BR>\n" );
document.write( "60a = 1 - 5<BR>\n" );
document.write( "a = -4/60<BR>\n" );
document.write( "a = -.0667<BR>\n" );
document.write( "Find b using b = -3a+1<BR>\n" );
document.write( "b = -3(-.0667) + 1<BR>\n" );
document.write( "b = .2 + 1<BR>\n" );
document.write( "b = 1.2<BR>\n" );
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document.write( "The equation for our arch: y = -.0667x^2 + 1.2x<BR>\n" );
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document.write( "Looks like this, green line is y = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+25%2C+-8%2C+16%2C+-.0667x%5E2%2B1.2x%2C+3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+25%2C+-8%2C+16%2C+-.0667x%5E2%2B1.2x%2C+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Axis of symmetry x=9<BR>\n" );
document.write( "Find max, the height of the arch<BR>\n" );
document.write( "y = -.0667(9^2) + 1.2(9)<BR>\n" );
document.write( "y = -5.4 + 10.8<BR>\n" );
document.write( "y = 5.4 meters is the height of the arch<BR>\n" );
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