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#1**+3 **

y = -0.000488x^2 + 0.656x

We have the form y = ax^2 + bx

The x coordinate of the vertex is = -b / [ 2 *a ] = - 0.656 / [ 2 * -0.000488 ] ≈ 672.13

To find the height above the river, put this value back into the function and we get

y = -0.000488(672.13)^2 + 0.656(672.13) ≈ 220.5 ft

The section of the bridge above the arch will be the difference between the intercepts of the function and the x axis

But (0,0) is one intercept...and using the fact that this parabola is symmetric bout its vertex point....the other intercept occurs at 2 ( 672.13) = 1344.26 ft ≈ 1344.3 ft.

See the graph, here : https://www.desmos.com/calculator/jd1toj6pak

[The line y = 220.5 represents the bridge span between the two x intercepts ]

CPhill Aug 17, 2018