Medicaid is characterized as:

Medicaid is defined as a combined federal and state program designed to provide health coverage for eligible low-income individuals and families. This program is jointly funded by both the federal government and the states, with states given the flexibility to design and implement their own Medicaid programs within the federal guidelines. As a result, each state may have different eligibility requirements, benefits, and payment structures, but they all must adhere to certain federal regulations to participate in the program.

The collaboration between federal and state governments is integral to Medicaid, allowing it to adapt to the varying healthcare needs of populations across different states. This collaborative approach also helps ensure that individuals who may not have access to healthcare coverage through other means, such as employment-based insurance, can receive necessary medical services.

The other options outline more narrow or incorrect definitions of Medicaid. It is not a federal program only, nor is it limited to veterans or children, which highlights why the correct characterization is that it is a combined federal and state program. This distinction is crucial for understanding Medicaid's role in the U.S. healthcare system and the variety of coverage it provides.