The equation of the parabola with vertex (0,0) and directrix y=-6 is given by: y = -1.5x².
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
The directrix is at y = k + 4a.
In this problem, we have that the vertex is (0,0), hence h = k = 0.
The directrix is y = -6, hence:
-6 = 4a
a = -6/4
a = -1.5.
Then the equation is:
y = -1.5x².
More can be learned about the equation of a parabola at https://brainly.com/question/26790601
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