**Core Concept**
The quadrilateral cartilage, also known as the quadrilateral ligament, is a fibrocartilaginous structure that plays a crucial role in the stability of the temporomandibular joint (TMJ). It is attached to various bony structures within the TMJ, contributing to its complex anatomy.

**Why the Correct Answer is Right**
The quadrilateral cartilage is attached to the articular tubercle of the mandible, the neck of the condyle, and the articular disc. This attachment is essential for the proper functioning of the TMJ, allowing for smooth movement and transmission of forces between the mandible and the skull. The quadrilateral cartilage helps to distribute the stresses and strains on the TMJ, ensuring the integrity and stability of the joint.

**Why Each Wrong Option is Incorrect**
* **Option B:** This option is incorrect because the quadrilateral cartilage is not attached to the coronoid process of the mandible. The coronoid process is a separate bony structure that serves as an attachment point for the temporalis muscle, which is involved in elevating the mandible.
* **Option C:** This option is incorrect because the quadrilateral cartilage is not attached to the zygomatic arch. The zygomatic arch is a bony structure that forms part of the lateral wall of the orbit, and it does not have a direct attachment to the quadrilateral cartilage.

**Clinical Pearl / High-Yield Fact**
The quadrilateral cartilage is often involved in temporomandibular joint disorders (TMDs), which can manifest as pain, limited jaw movement, or clicking sounds. Understanding the anatomy and function of the quadrilateral cartilage is essential for diagnosing and managing TMDs.

**Correct Answer: D.**