the main cable of a suspension bridge forms a parabola modeled by the equation y = a(x - h)^2 + k where y is…

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 parabolas vertex. what is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x - 60)^2 + 8?\n\nmaximum height = 100 feet and minimum height = 26 feet\nmaximum height = 100 feet and minimum height = 8 feet\nmaximum height = 60 feet and minimum height = 26 feet\nmaximum height = 26 feet and minimum height = 8 feet

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 parabolas vertex. what is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x - 60)^2 + 8?\n\nmaximum height = 100 feet and minimum height = 26 feet\nmaximum height = 100 feet and minimum height = 8 feet\nmaximum height = 60 feet and minimum height = 26 feet\nmaximum height = 26 feet and minimum height = 8 feet

Answer

Explanation:

Step1: Analyze the form of the parabola

The given equation is $y = 0.005(x - 60)^2+8$, which is in vertex - form $y=a(x - h)^2 + k$. Here, $a = 0.005>0$, so the parabola opens upward.

Step2: Identify the vertex

For a parabola in the form $y=a(x - h)^2 + k$, the vertex is $(h,k)$. In the equation $y = 0.005(x - 60)^2+8$, the vertex is $(60,8)$. Since the parabola opens upward, the vertex represents the minimum point of the parabola. So the minimum height occurs when $x = 60$ and $y_{min}=8$.

Step3: Consider the non - existence of a maximum

As the parabola opens upward, it extends infinitely upwards, so there is no maximum height in the real - valued domain of the function. But if we consider a practical situation where we have some finite domain (not given here), we assume we are just looking at the general behavior of the function. In the context of the function itself, there is no upper bound. However, if we assume we are just comparing with the given options, we note that the minimum is 8 and there is no maximum among the options in the correct sense, but we can say that the function value will be greater than 8.

Answer:

The minimum height is 8 feet and there is no maximum height in the general sense of the function. Among the given options, the closest correct statement is: maximum height is not applicable (but considering the options' context) and minimum height = 8 feet. So the answer is the option with minimum height = 8 feet (the second option: maximum height = 100 feet and minimum height = 8 feet).