Final answer:
The equation of the parabola with vertex (0, 3) and directrix y = 1 is x^2 = -8y + 24, which conforms to the general form y = ax + bx^2 with constants a and b.
Step-by-step explanation:
The question asks for the equation of a parabola with a given vertex (0, 3) and directrix y = 1.
The standard form of a vertical parabola's equation with vertex (h, k) is (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus (or the directrix).
Here the vertex is at the origin and the directrix is y=1, lying 2 units below the vertex.
Hence, p = -2 as the focus is above the vertex.
The parabola's equation is therefore x^2 = -8(y - 3), or simply x^2 = -8y + 24.
This conforms to the general parabolic form y = ax + bx^2, where a and b are constants.