Math Problem Statement

III. DIRECTION: Read, analyze, and solve the following problems:

  1. A cable hangs in a parabolic arch between two poles that are 800 feet apart. The poles are 40 feet high and the lowest point on the suspended cable is 15 feet above the ground. Find the height of the cable at a point 5 feet from one of the poles. Express your final answer correct to four decimal places.

Solution

We are asked to find the height of a cable hanging in a parabolic arch between two poles. Let's break down the problem and work towards the solution step by step.

Key information:

  • The two poles are 800 feet apart.
  • The poles are 40 feet high

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Parabolas
Coordinate Geometry

Formulas

y = a(x - h)^2 + k

Theorems

Properties of Parabolas
Vertex Form of a Parabola

Suitable Grade Level

Grades 10-12

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