Answer:
y = 0.0633 x^2
Explanation:
Since the vertex of the parabola is at the origin, the equation of the parabola can be written in the form:
y = a x^2
where a is a constant that determines the shape of the parabola.
The focus of the parabola is at the point (0,-7.9). Recall that the focus of a parabola is a point that is equidistant from the vertex and the directrix. Since the vertex is at the origin, the directrix must be a horizontal line that is 7.9 units above the vertex. Therefore, the equation of the directrix is:
y = 7.9
The distance between the vertex and the focus is equal to the distance between the vertex and the directrix. This distance is given by:
d = |-7.9 - 0|/2 = 3.95
Therefore, the constant a can be found by solving the equation:
a = 1/(4d) = 1/(4(3.95)) = 0.0633
So the equation of the parabola is:
y = 0.0633 x^2