Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 142 feet and a maximum height of 25 feet. Find the height of the arch at 25 feet from its center.
A) 21.9 ft
B) 0.8 ft
C) 71 ft
D) 12.4 ft

Question

Quizplus · Accepted Answer

The equation of a parabolic arch can be represented as $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Given the maximum height of the arch is 25 feet, this means $k = 25$. The span of the bridge is 142 feet, so the vertex is at the center, making $h = 0$. The distance from the center to either end is 71 feet, so when $x = 71$, $y = 0$. We can use this information to find $a$: $0 = a(71)^2 + 25$, solving for $a$ gives $a \approx -0.00496$. To find the height at 25 feet from the center, substitute $x = 25$ into the equation: $y = -0.00496(25)^2 + 25$, which gives $y \approx 21.9$.

Solve the Problem. -A Bridge Is Built in the Shape of a Parabolic