Solve Applied Problems Involving Parabolas
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 184 feet and a maximum height of 40 feet. Find the height of the arch at 15 feet from its center.
A) $38.9 \mathrm { ft }$
B) $0.3 \mathrm { ft }$
C) $4.3 \mathrm { ft }$
D) $12.9 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The equation of a parabola in vertex form is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Given the maximum height of the arch is 40 feet, this means the vertex is at $(0, 40)$ because the maximum height is at the center of the span. The span of the bridge is 184 feet, so the roots of the parabola are at $\pm 92$ feet from the center. We can use one of the roots, say $(92, 0)$, to find the value of $a$. Substituting into the vertex form, we get $0 = a(92)^2 + 40$, solving for $a$ gives $a = -40/92^2$. To find the height at 15 feet from the center, substitute $x = 15$ into the equation: $y = -40/92^2 \cdot 15^2 + 40$, which calculates to approximately $38.9$ feet.

Solve Applied Problems Involving Parabolas -A Bridge Is Built in the Shape

Solve Applied Problems Involving Parabolas
-A Bridge Is Built in the Shape