What is the vertex of the parabola defined by the equation

(x - 2) 2 = - 12 (y - 2) ?

A.

(-12, 2)

B.

(2, 2)

C.

(6, 2)

D.

(2, - 2)

The vertex of the parabola is (2, 2) ⇒ answer B

Step-by-step explanation:

* Lets revise the equation of a parabola

- The equation is in the form (x - h) ² = 4p (y - k), where h and k are the

vertex of the parabola

- If p > 0, the parabola opens up

- If p < 0, the parabola opens down

* Lets solve the problem

∵ The equation of the parabola is (x - h) ² = 4p (y - k)

∵ The equation of the parabola is (x - 2) ² = - 12 (y - 2)

- By comparing the two equations

∴ 4p = - 12 ⇒ divide both sides by 4

∴ p = - 3 ⇒ - 3 < 0

∵ p < 0

∴ The parabola opens down

- From the two equations

∴ h = 2 ⇒ the x-coordinate of the vertex

∴ k = 2 ⇒ the y-coordinate of the vertex

∴ The vertex of the parabola is (2, 2)