1. The problem states that the average gas mileage $y$ of new vehicles sold in Switzerland from 2013 to 2019 is modeled by the quadratic function $$y = -0.4(x - 3)^2 + 42,$$ where $x$ is the number of years since 2013. 2. We are asked to find the year when the average gas mileage was the greatest. 3. Since the function is a quadratic with a negative leading coefficient ($-0.4$), it opens downward, meaning the vertex represents the maximum point. 4. The vertex form of a quadratic is $$y = a(x - h)^2 + k,$$ where $(h, k)$ is the vertex. 5. From the given equation, the vertex is at $(3, 42)$. 6. The $x$-value of the vertex is $3$, which means 3 years after 2013. 7. Therefore, the year when the average gas mileage was greatest is $$2013 + 3 = 2016.$$