Question

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

( y=\frac{1}{4}(x + 4)^{2} )

the vertex is
(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.
For the given equation \(y=\frac{1}{4}(x + 4)^2\), we can rewrite it as \(y=\frac{1}{4}(x-(-4))^2+0\).

Step2: Identify the vertex

Comparing with \(y = a(x - h)^2 + k\), we have \(h=-4\) and \(k = 0\).

Answer:

\((-4,0)\)