The correct answer is option 'C', which states that the most commonly designed highway vertical curve is a parabolic curve. In this answer, we will explain why parabolic curves are commonly used in highway design and discuss the advantages of using this type of curve.

Parabolic curves in highway design:

1. Definition:
A parabolic curve is a vertical curve that follows a parabolic path. It is a smooth curve that connects two different grades on a highway, allowing for a gradual change in elevation.

Advantages of using parabolic curves:

1. Smooth transition:
Parabolic curves offer a smooth and continuous transition between two different grades. This ensures that vehicles can safely navigate the curve without experiencing sudden changes in elevation, which could lead to discomfort or accidents.

2. Comfortable driving experience:
The use of parabolic curves helps provide a comfortable driving experience for motorists. By maintaining a consistent rate of change in elevation, parabolic curves minimize the vertical acceleration experienced by drivers and passengers. This reduces discomfort and fatigue during travel.

3. Efficient drainage:
Parabolic curves are designed to ensure efficient drainage of water from the highway surface. The shape of the curve allows for the effective runoff of rainwater, preventing pooling and improving overall road safety.

4. Cost-effective design:
Parabolic curves are often more cost-effective compared to other types of curves. They require less earthwork and grading compared to spiral or compound curves, reducing construction costs and time.

5. Compatibility with design standards:
Parabolic curves are widely used in highway design because they conform to the standards and guidelines set by transportation authorities. These curves are recommended by design manuals and codes, ensuring consistency and uniformity in highway design practices.

In conclusion, the most commonly designed highway vertical curve is a parabolic curve. It offers several advantages, including a smooth transition, comfortable driving experience, efficient drainage, cost-effectiveness, and compliance with design standards. By using parabolic curves in highway design, transportation authorities can ensure safe and efficient travel for motorists.