Which description correctly states the role of the coefficient a in y = ax^2 + bx + c?

Coefficient a determines both the frequency of oscillation of the parabola and the scale of its x-intercepts, serving as a periodicity parameter analogous to coefficients in trigonometric functions.

Coefficient a only affects the intercept on the y-axis and has no effect on curvature or vertex location; the vertex is entirely determined by b alone.

The coefficient a controls curvature and concavity: a>0 gives a U-shaped (concave up) parabola, a<0 gives an upside-down U (concave down); |a| controls how 'steep' or 'wide' the parabola is.

The coefficient a shifts the parabola left or right along the x-axis and does not affect its width or whether it opens up or down; shifting is controlled purely by b and c.