Match the Function y=-(x+2)² to its Corresponding Graph

One function

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

for the corresponding chart

The function $y = -(x+2)^2$ represents a downward-opening parabola with the vertex at $(-2, 0)$. This transformation involves a horizontal shift to the left by 2 units from the origin.

• The vertex form of a quadratic function is $y = a(x-h)^2 + k$, where $(h, k)$ represents the vertex.
• In our function, $h = -2$ and $k = 0$, so the vertex is $(-2, 0)$.
• The coefficient of $-1$ indicates that the parabola opens downward.
• Since the vertex $(-2, 0)$ and the downward opening are correctly depicted in graph 3, this aligns with our function.

Therefore, after comparing the characteristics of the function with the given graphs, the corresponding graph for this function is option 3.