document.write( "Question 1203474: Bridge shaped like a parabolic arch has a horizontal distance of 20 feet. The height of a point 1 foot from the center is 8 feet. What is the maximum height of the bridge if it is located at the center? \n" ); document.write( "

Algebra.Com's Answer #839075 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The two responses you have received to this point show variations of a standard formal algebraic solution.

\n" ); document.write( "Here is a different, informal method which can sometimes make solving problems like this easier (and sometimes not!)

\n" ); document.write( "Since the shape is a parabola, the change in the y value from the axis of symmetry is proportional to the square of the corresponding change in the x value.

\n" ); document.write( "The height of the arch is on the axis of symmetry, which we can consider to be x=0.

\n" ); document.write( "Let h be the height of the arch -- i.e., the vertex of the parabola is at (0,h). The point (1,8) on the arch is 1 unit horizontally and (h-8) units vertically from the top of the arch; the point (10,0) is 10 units horizontally and h units vertically from the top of the arch.

\n" ); document.write( "The second point is 10 times as far from the axis of symmetry as the first, so the difference in the vertical distance from 0 to the top of the arch should be 100 times the difference in the vertical distance from (1,8) to the top of the arch:

\n" ); document.write( " $\"h=100%28h-8%29\"$
\n" ); document.write( " $\"h=100h-800\"$
\n" ); document.write( " $\"99h=800\"$
\n" ); document.write( " $\"h800%2F99\"$ = 8.0808...

\n" ); document.write( "ANSWER: The height of the arch is 8.08 feet, to 2 decimal places.
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