Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 154 feet and a maximum height of 30 feet. Find the height of the arch at 20 feet from its center.
A) 34.2 ft
B) 0.5 ft
C) 28 ft
D) 8.1 ft

Question

Quizplus · Accepted Answer

The equation of a parabolic arch can be represented as $y = ax^2 + bx + c$. Given the maximum height of the arch is at the center, we can assume the vertex of the parabola is at the origin (0, 30), simplifying the equation to $y = ax^2 + 30$. The span of the bridge being 154 feet means the roots of the equation are at $x = -77$ and $x = 77$, since the total span is centered around the origin. To find the value of $a$, we use one of the roots: $0 = a(77)^2 + 30$, solving for $a$ gives us $a = -30/77^2$. To find the height at 20 feet from the center, substitute $x = 20$ into the equation: $y = (-30/77^2)(20)^2 + 30$, which simplifies to approximately 28 feet.

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