Find the Vertex of y=(x+2)²-3: Parabola Analysis

Find the vertex of the parabola

$y=(x+2)^2-3$

To find the vertex of the parabola given by the equation $y = (x+2)^2 - 3$, we will use our understanding of the vertex form of a quadratic equation.

The vertex form of a quadratic equation is expressed as:

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

In this formula, the vertex of the parabola is located at the point $(h, k)$.

Now, let's compare the given equation $y = (x+2)^2 - 3$ with the standard vertex form:

• Notice that the expression inside the bracket is $(x+2)$. This can be rewritten as $(x - (-2))$, which highlights that $h = -2$.
• The constant term at the end is $-3$, which corresponds to $k = -3$.

Therefore, the vertex of the parabola is $(-2, -3)$.

Checking against the provided choices, the correct answer is option 1: $(-2, -3)$.

Thus, we conclude that the vertex of the parabola is $(-2, -3)$.