Question

What is the vertex of the parabola defined by the equation
(x - 2)2 = -12(y - 2)?

Answer 1

(2, 2).

Explanation:

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

Convert to vertex form:

x^2 - 4x + 4 = -12y + 24

-12y = x^2 - 4x - 20

y = (-1/12) (x^2 - 4x - 20)

y = -1/12 (x - 2)^2 - 4 - 20)

= -1/12 (x - 2)^2 + 2

So the vertex is (2, 2).

Answer 2

(2, 2 )

Explanation:

The equation of a parabola in the form

(x - h)² = 4p(y - k) is the equation of a vertically opening parabola

with vertex = (h, k )

(x - 2)² = - 12(y - 2) is in this form

with h = 2 and k = 2, hence

vertex = (2, 2 )