Question

The cables on a suspension bridge can be modeled by h = 0.0088x2 − 0.88x + 40, where h is the height in feet of the cable above the roadway x feet from the start of the bridge. What is the minimum height of the cables above the roadway?

Answer 1

The minimum height of the cables above the roadway is 62 feet, which is found by identifying the vertex of the parabola represented by the equation h = 0.0088x^2 - 0.88x + 40.

Step-by-step explanation:

To find the minimum height of the cables above the roadway, we need to identify the vertex of the parabola represented by the quadratic equation h = 0.0088x2 - 0.88x + 40. This equation is in the standard form of a quadratic equation, h = ax2 + bx + c, where the x-coordinate of the vertex can be found using the formula -b/(2a). In this equation, a is 0.0088 and b is -0.88.

Plugging these values into the vertex formula gives x = -(-0.88) / (2 * 0.0088) = 50. Therefore, the x-coordinate of the vertex is 50 feet. Now, substituting x back into the original equation gives us the height: h = 0.0088(50)2 - 0.88(50) + 40 = 0.0088(2500) - 44 + 40 = 22 + 40 = 62 feet. The minimum height of the cables above the roadway is 62 feet, which occurs directly above the vertex of the parabola.