document.write( "Question 274639: A bridge is built in the shape of a parabolic arch. The bridge has a span of 50 metres and a maximum height of 40 metres. Find the height of the arch 10 metres from the center.\r
\n" ); document.write( "\n" ); document.write( "Please & Thank you, i can't even begin to think about how to answer this question. \n" ); document.write( "
Algebra.Com's Answer #200465 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A bridge is built in the shape of a parabolic arch.
\n" ); document.write( " The bridge has a span of 50 metres and a maximum height of 40 metres.
\n" ); document.write( " Find the height of the arch 10 metres from the center.
\n" ); document.write( ":
\n" ); document.write( "Here's an idea of what this will look like, where x = the length & y = the height of the bridge
\n" ); document.write( " \"+graph%28+300%2C+200%2C+-10%2C+65%2C+-10%2C+50%2C+-.064x%5E2%2B3.2x%29+\"
\n" ); document.write( ":
\n" ); document.write( "We want to find the quadratic equation for this parabola using the form:
\n" ); document.write( "ax^2 + bx + c = y; c = 0, so we only have to find a and b
\n" ); document.write( ";
\n" ); document.write( "We need two x/y coordinates, from the information given.
\n" ); document.write( ":
\n" ); document.write( "max height is half way: 25 meters and is 40 meters is the height
\n" ); document.write( "x = 25, y = 40
\n" ); document.write( "25^2a + 25b = 40
\n" ); document.write( "625a + 25b = 40
\n" ); document.write( "and
\n" ); document.write( "the span is given as 50 m and then height = 0
\n" ); document.write( "x = 50, y = 0
\n" ); document.write( "50^2a + 50b = 0
\n" ); document.write( "2500a + 50b = 0
\n" ); document.write( ":
\n" ); document.write( "we have two equations to find two unknowns, use elimination
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 2, and subtract it from the above equation
\n" ); document.write( "2500a + 50b = 0
\n" ); document.write( "1250a + 50b = 80
\n" ); document.write( "-------------------subtraction eliminates b, find a
\n" ); document.write( "1250a = -80
\n" ); document.write( "a = \"%28-80%29%2F1250\"
\n" ); document.write( "a = -.064
\n" ); document.write( ":
\n" ); document.write( "Find b using the 1st equation, substitute -.064 for a
\n" ); document.write( "-.064(625) + 25b = 40
\n" ); document.write( "-40 + 25b = 40
\n" ); document.write( "25b = 40 + 40
\n" ); document.write( "25b = 80
\n" ); document.write( "b = \"80%2F25\"
\n" ); document.write( "b = 3.2
\n" ); document.write( ":
\n" ); document.write( "The equation for this parabola: y = -.064x^2 + 3.2x
\n" ); document.write( ":
\n" ); document.write( "\"Find the height of the arch 10 metres from the center.\"
\n" ); document.write( ":
\n" ); document.write( "there are two points, 10 meters from the center which is 25 m:
\n" ); document.write( "15 meters, substitute 15 for x in our equation, find y (height)
\n" ); document.write( "y = -.064(15^2) + 3.2(15)
\n" ); document.write( "y = -.064(225) + 3.2(15)
\n" ); document.write( "y = -14.4 + 48
\n" ); document.write( "y = 33.6 m, 10 meters left of the center
\n" ); document.write( ":
\n" ); document.write( "How about 10 meter right of center, 35 m?
\n" ); document.write( "y = -.064(35^2) + 3.2(35)
\n" ); document.write( "y = -.064(1225) + 3.2(35)
\n" ); document.write( "y = -78.4 + 112
\n" ); document.write( "y = 33.6 m, 10 meters right of the center, same as you would expect in a parabola
\n" ); document.write( ":
\n" ); document.write( "You can see this agrees with the graph (generated by the equation we just created)
\n" ); document.write( ":
\n" ); document.write( "Hopefully, this shed some light on this problem for you.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );