Answer:
The option that could be equation of the parabola is;
x² = 4·y
Step-by-step explanation:
The location of the vertex of the parabola = (0, 0)
The location of the directrix of the parabola = The negative part of the y-axis
Given that the directrix crosses the y-axis, the directrix can be taken as being parallel to the y-axis, and the equation of the directrix presented as follows;
y = k - p
Therefore, the general equation of the parabola is of the following form;
(x - h)² = 4·p·(y - k)
Given that the directrix, y = k - p is negative, and the vertex, (h, k) = (0, 0) therefore;
h = 0, k = 0
y = k - p = 0 - p = -p
y = -p (negative), therefore, 'p' = Positive > 0
The equation of the parabola becomes;
(x - 0)² = 4·p·(y - 0)
∴ x² = 4·p·y
Where p = 1 (assumption), we get the possible equation of the parabola presented as follows;
x² = 4·y.