Question

You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y= -0.000475x^2 + 0.851x, where x and y in feet. How high above is the river bridge (the top of the arch)? How long is section of bridge above the arch?

A)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.

B)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

C)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.

D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft

Answer 1

y= -0.000475x^2 + 0.851x

How high above is the river bridge (the top of the arch)?

You have to find the vertex of of the parabole: the y-coordinate is the highest point.

Remember that the x-coordinate of the vertex of a parabole is at - b / 2a.

That is  x = - 0.851 / [ 2(-0.000475) = 895.79

The corresponden y is y = -0.000475(895.79)^2 + 0.851(895.79) = 381.16 feet above the river.

How long is section of bridge above the arch?

The section of the brige is equal to the difference of the two roots

Roots: y= -0.000475x^2 + 0.851x = 0

=> x( - 0.000475x + 0.851) = 0

=> x = 0 and x = 0.851 / 0.000475 = 1791.58

Then the section is 1791.58 feet long.

Therefore, the answer is the option D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft