Find the Vertex of y=(x+2)²-2: Quadratic Function Analysis

Find the vertex of the parabola

$y=(x+2)^2-2$

To solve the problem of finding the vertex of the parabola represented by $y = (x+2)^2 - 2$, consider the form of the equation.

This equation is written in the vertex form of a quadratic function, which is given by:

$y = a(x-h)^2 + k$

where $(h, k)$ is the vertex of the parabola.

Comparing $y = (x+2)^2 - 2$ with the standard form $y = a(x-h)^2 + k$, we identify:

• $h = -2$ because the expression is $(x - (-2))^2$
• $k = -2$

Therefore, the vertex of the parabola is $(-2, -2)$.

The correct answer is $(-2, -2)$.