The main cable of a suspension bridge forms a parabola modeled by the equation y = a(x – h)2 + k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, a is a constant, and (h, k) is the parabola’s vertex. What is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x – 60)2 + 8?

maximum height = 100 feet and minimum height = 26 feet
maximum height = 100 feet and minimum height = 8 feet
maximum height = 60 feet and minimum height = 26 feet
maximum height = 26 feet and minimum height = 8 feet

The equation given, y = 0.005(x – 60)2 + 8, represents the height of the suspension bridge's main cable above the road. To find the maximum and minimum height of the bridge, we need to identify the vertex of the parabola.

In general, the vertex of a parabola in the form y = a(x - h)2 + k is represented by the point (h, k). In this case, the vertex is (60, 8), which means the bridge is highest at a horizontal distance of 60 feet from the right bridge support.

To determine the maximum and minimum heights of the bridge, we can consider the value of "a" in the equation. Since "a" is positive (0.005), the parabola opens upwards, indicating a minimum value at the vertex and no maximum value.

Therefore, the minimum height of the bridge is 8 feet, occurring at a horizontal distance of 60 feet from the right bridge support.