vertex = (2, 2)
the equation of a parabola opening vertically is
(x - h)² = 4p(y - k)
where (h, k) are the coordinates of the vertex and p is the distance from the vertex to the focus
(x - 2)² = - 12(y - 2) is in this form
with vertex = (2, 2)
The vertex of the given parabola [tex](x -2)^{2} = - 12(y - 2)[/tex] is (2, 2).
The general form of a parabola opening vertically is:
(x - h)² = 4p(y - k)
Here, (h, k) are the coordinates of the vertex.
'p' is the distance between the focus and the vertex.
If p > 0, the parabola opens upwards.
If p < 0, the parabola opens downwards.
The given equation of a parabola is: (x - 2)² = - 12(y - 2)
Therefore, comparing the given equation with the general equation of parabola, the vertex of the given parabola is (2, 2).
Again, 4p = - 12
⇒ p = - 3
As p < 0, therefore, the parabola opens downwards.
Learn more about parabola here: https://brainly.com/question/12841078
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