Match the Quadratic Function y=(x+3)² with its Corresponding Graph

To solve this problem, we'll proceed as follows:

• Step 1: Identify the vertex of the function $y=(x+3)^2$.
• Step 2: Determine the direction the parabola opens.
• Step 3: Compare the features of each choice's graph to the characteristics identified.

Let's analyze the function $y=(x+3)^2$:

Step 1: The vertex of the function $y=(x+3)^2$ is at $(p, 0)$. Since $p = -3$, the vertex is at the point $(-3, 0)$.

Step 2: The function is of the form $y=(x+3)^2$, which opens upwards because the coefficient of $(x+3)^2$ is positive.

Step 3: By comparing graphs, we select the one where the parabola has a vertex at $(-3, 0)$ and opens upwards. Looking at the provided choices, choice 4 has a graph with a vertex at $(-3, 0)$ and is consistent with the function opening upwards.

Therefore, the correct graph corresponding to the function $y=(x+3)^2$ is choice 4.