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)