Question

determine the vertex, focus, and directrix for the following parabola.

( y = 2 ( x - 3 ) ^ { 2 } - 21 )

the vertex is
(simplify your answer. type an ordered pair.)

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h,k)\) is the vertex.

Step2: Identify \(h\) and \(k\)

For the given equation \(y = 2(x - 3)^2-21\), we have \(h = 3\) and \(k=-21\).

Answer:

\((3,-21)\)