https://file.aiquickdraw.com/mathbot/file/1727928159653s05g15g6.jpg

The problem in the image involves a bridge supported by a parabolic arc, and we are tasked with determining the height of posts at regular intervals along the arc.

### Problem Summary:
- The bridge forms a parabolic arc.
- The highest posts are 10 meters tall, located at the ends of the bridge.
- The arc’s highest point (vertex) is 6 meters above the base of the bridge.
- The distance between the tallest posts (end to end) is 60 meters.
- We need to find the height of posts every 10 meters along the bridge.

### Steps to Solve:
We can model the parabolic arc as a quadratic equation of the form:
\[
y = ax^2 + bx + c
\]
where:
- \(y\) represents the height of the posts at any given position \(x\),
- \(x\) is the horizontal distance from the center of the bridge,
- The highest point (vertex) is at the center, so \(x = 0\) corresponds to the center of the bridge.
- The total span of the bridge is 60 meters, so the end points are \(x = -30\) and \(x = 30\).

### Key Conditions:
1. At the highest point (vertex), \(x = 0\), \(y = 6\) meters.
2. At the ends of the bridge, \(x = -30\) and \(x = 30\), \(y = 10\) meters.

We’ll find the quadratic equation based on these conditions and calculate the heights at intervals of 10 meters.

Let me work this out.

A bridge is supported below by a reinforced arc in the shape of a parabola. The highest posts measure 10 meters from the foot of the bridge, and the arc reaches a height of 6 meters. The distance between the tallest posts is 60 meters. What should be the size of the posts every 10 meters along the bridge?

Calculate the heights of support posts along a parabolic bridge using the quadratic equation. This problem involves determining post heights at intervals of 10 meters based on a parabola’s arc, with a maximum height of 6 meters at the center. Suitable for high school students.

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