Final answer:
The 1912 election of Theodore Roosevelt best demonstrates the influence of the Progressive Party.
Step-by-step explanation:
The election that best demonstrates the influence of the Progressive Party is A. the 1912 election of Theodore Roosevelt. Roosevelt attempted to form a third party known as the Progressive Party as an alternative to the Republicans. The Progressives sought to make government more responsive to the people and address issues like women's suffrage, an eight-hour workday, and workers' compensation.
Theodore Roosevelt's decision to run under the Progressive Party banner resulted in a significant split in the Republican vote, leading to the election of Democrat Woodrow Wilson.
Additionally, the Progressive Party's platform was influential in shaping the policies and directions of both the Republican and Democratic parties in subsequent years, particularly impacting President Wilson's administration with Progressive ideas.
However, most members eventually returned to the Republican Party and the Progressive Party shortly faded from the national political stage.