The arch of the railroad track bridge below is in the shape of a parabola.

The two main supporters are apart distance is .

The length of main supporters is .

The distance from the top of the parabola to the water below is .

If the railroad track represents the -axis, then the vertex lies on the -axis.

The difference between verical distances is .

(a) Find the equation of parabola.

The parabola is vertical parabola and opens down.

The vertex is .

The arch meets each support tower to the left and to the right of the vertex and below the railroad or the - axis.

Thus, two points on the parabola are at and .

The standard form of vertical parabola is .

Substitute and .

.

Substitute and in .

.

The equation of parabola is .

(b) Find their lengths if they are apart.

Two vertical supporters are attached to the arch are equidistant from the center is .

The distance between center and vertical supporte is .

Find when .

Substitute in .

.

The supporters met the parabola at the points and .

The length of the vertical supporters is .

(a) The equation of parabola is .

(b) The length of the vertical supporters is .