Question

1. $y = 2(x + 4)^2 + 2$

Explanation:

Assuming the problem is to identify the vertex of the parabola given by the equation \( y = 2(x + 4)^2 + 2 \), we can use the vertex form of a parabola.

Step 1: 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 of the parabola.

Step 2: Compare the given equation with the vertex form

Given equation: \( y = 2(x + 4)^2 + 2 \)
We can rewrite \( x + 4 \) as \( x - (-4) \), so the equation becomes \( y = 2(x - (-4))^2 + 2 \)

Step 3: Identify \( h \) and \( k \)

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

Answer:

The vertex of the parabola \( y = 2(x + 4)^2 + 2 \) is \((-4, 2)\)