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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)

1 Answer

6 votes

Answer:

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

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)

User Anatoly  Vdovichev
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