To find the vertex of the given parabola defined by the equation [tex]\((x-2)^2 = -12(y-2)\)[/tex], we can follow these steps:
1. Identify the standard form of the parabola equation: The given equation is [tex]\((x-2)^2 = -12(y-2)\)[/tex]. For comparison, recall the standard form of a parabola that opens vertically: [tex]\((x-h)^2 = 4p(y-k)\)[/tex], where [tex]\((h, k)\)[/tex] represents the vertex of the parabola.
2. Compare the given equation to the standard form: By comparing [tex]\((x-2)^2 = -12(y-2)\)[/tex] to [tex]\((x-h)^2 = 4p(y-k)\)[/tex], we can identify the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex]:
- The term [tex]\((x-2)\)[/tex] indicates that [tex]\(h = 2\)[/tex].
- The term [tex]\((y-2)\)[/tex] indicates that [tex]\(k = 2\)[/tex].
3. Determine the vertex: From our comparison, we see that the values [tex]\(h\)[/tex] and [tex]\(k\)[/tex] represent the coordinates of the vertex of the parabola. Thus, the vertex of the parabola [tex]\((x-2)^2 = -12(y-2)\)[/tex] is [tex]\((2, 2)\)[/tex].
Therefore, the correct answer is:
B. [tex]\((2, 2)\)[/tex]
