Choice A is the correct answer. A quadratic function has a maximum value only if it opens downward.

1. Check the leading coefficient $a$ for each option.
2. A: $a = -2$ (Negative $\rightarrow$ Opens Down $\rightarrow$ Maximum).
3. B: $a = 1$ (Positive $\rightarrow$ Opens Up $\rightarrow$ Minimum).
4. C: $a = 3$ (Positive).
5. D: $a = 0.5$ (Positive).

Choice B is incorrect because $a > 0$. Choice C is incorrect because $a > 0$. Choice D is incorrect because $a > 0$.