Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers stand 50 inches apart. At a point between the towers and 15 inches along the road from the
Base of one tower, the cable is 1 inches above the roadway. Find the height of the towers.
A) 6.75 in.
B) 5.75 in.
C) 6.25 in.
D) 8.25 in.

Question

Quizplus · Accepted Answer

The height of the towers can be found by using the vertex form of a parabolic equation, $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Since the towers are 50 inches apart and the cable touches the roadway exactly between them, the vertex is at the midpoint, 25 inches from each tower, and at the roadway level. The point given, 15 inches from one tower and 1 inch above the roadway, provides a way to solve for $a$. Substituting $x = 15$, $y = 1$, and knowing the vertex is at $(25, 0)$ (shifting the coordinate system for simplicity), we get $1 = a(15 - 25)^2$, leading to $a = 1/100$. The height of the towers is the value of $y$ when $x = 0$ or $x = 50$, which gives $y = a(25)^2 = (1/100)(625) = 6.25$.

Solve the Problem. -An Experimental Model for a Suspension Bridge Is Built in Is