Final answer:
The coefficient 'a' in the general or vertex form of a parabola determines its direction. When a < 0, the parabola opens downwards, creating a shape like an upside-down 'U' or a 'frown.' The correct answer is B.
Step-by-step explanation:
When analyzing the general or vertex form of a parabola, specifically given by the equation y = ax2 + bx + c, the coefficient a plays a critical role in determining the direction in which the parabola opens. If a < 0, the parabola opens downwards, characterized by a 'frown-like' shape. This is because the negative value of a in the quadratic term will result in the parabola having a maximum point, after which the values of 'y' decrease as 'x' moves away from the vertex in either direction.
It is important to mention that the sign of coefficient 'a' does not affect the position of the vertex itself or whether the axis of symmetry is vertical. Those characteristics are determined by other components of the equation. The axis of symmetry is always vertical for a parabola represented in the general or vertex form and the actual position of the vertex is given by the values derived from coefficients 'a', 'b', and 'c' through formulas or completing the square if in general form.