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If $$y = ax^2 + bx + c$$, $$a \ne 0$$, then $$y = a\left(x + \frac{b}{2a}\right)^2 + \frac{4ac - b^2}{4a}$$
The term $$\left(x + \frac{b}{2a}\right)^2 \ge 0$$ and equals 0 at $$x = -\frac{b}{2a}$$. If $$a > 0$$, $$y \ge \frac{4ac - b^2}{4a}$$, so this is the minimum value and $$y$$ has no maximum. If $$a < 0$$, $$y \le \frac{4ac - b^2}{4a}$$, so this is the maximum value. Hence options a and d are both correct.
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