document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199007>Question 199007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parabolic arch has a span of 120 feet and a maximum height of 25 feet.  Choose a suitable rectangular coordinate system and find the equation of the parabola.  Then calculate the height of the arch 10, 20 and 40 feet from the center.  Provide a sketch representing the situation and be sure it is clearly labeled with coordinates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149528 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=149528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A parabolic arch has a span of 120 feet and a maximum height of 25 feet.<BR>\n" );
document.write( " Choose a suitable rectangular coordinate system and find the equation of the<BR>\n" );
document.write( " parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center.<BR>\n" );
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document.write( "Find the equation using the format y = ax^2 + bx + c (c=0, we can ignore that)<BR>\n" );
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document.write( "Using the vertex <BR>\n" );
document.write( "x=60, y = 25<BR>\n" );
document.write( "a(60^2) + 60b = 25<BR>\n" );
document.write( "3600a + 60b = 25<BR>\n" );
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document.write( "Using the x intercept<BR>\n" );
document.write( "x=120, y=0<BR>\n" );
document.write( "a(120^2) + 120b = 0<BR>\n" );
document.write( "14400a + 120b = 0<BR>\n" );
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document.write( "Multiply the 1st equation by 2, subtract from the 2nd equation<BR>\n" );
document.write( "14400a + 120b = 0<BR>\n" );
document.write( " 7200a + 120b = 25<BR>\n" );
document.write( "--------------------subtraction eliminates b, find a<BR>\n" );
document.write( "7200a = -25<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25%2F7200 ALIGN=MIDDLE  ALT=\"-25%2F7200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.00694<BR>\n" );
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document.write( "Find b using the 2nd equation, substitute -.00694 for a<BR>\n" );
document.write( "14400(-.00964) + 120b = 0<BR>\n" );
document.write( "-100 + 120b = 0<BR>\n" );
document.write( "120b = 100<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F120 ALIGN=MIDDLE  ALT=\"100%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = .833<BR>\n" );
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document.write( "y = -.00694x^2 + .8333x; the equation for this parabola<BR>\n" );
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document.write( "10 ft from center: 60-10 = 50 = x<BR>\n" );
document.write( "y = -.00694(50^2) + .8333(50)<BR>\n" );
document.write( "y = -17.35 + 41.665<BR>\n" );
document.write( "y = 24.3 ft high, 10 ft from center<BR>\n" );
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document.write( "20 ft from center: 60-20 = 40 = x<BR>\n" );
document.write( "y = -.00694(40^2) + .8333(40)<BR>\n" );
document.write( "y = -11.1 + 33.3<BR>\n" );
document.write( "y = 22.2 ft high. 20 ft from center<BR>\n" );
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document.write( "40 ft from center: 60-40 = 20 = x<BR>\n" );
document.write( "y = -.00694(20^2) + .8333(20)<BR>\n" );
document.write( "y = -2.8 + 16.7<BR>\n" );
document.write( "y = 13.9 ft high. 40 ft from center<BR>\n" );
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document.write( "The graph of this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+130%2C+-10%2C+30%2C+-.00694x%5E2%2B.833x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+130%2C+-10%2C+30%2C+-.00694x%5E2%2B.833x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( " Provide a sketch representing the situation and be sure it is clearly labeled with coordinates.\r<BR>\n" );
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document.write( "Your sketch should resemble this graph, you should be able to label this now </SPAN>\n" );
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