Identify the Graph of y=(x+1)²: Quadratic Function Matching

One function

$y=(x+1)^2$

for the corresponding chart

The provided function is $y = (x + 1)^2$, a parabola opening upwards. The vertex of this parabola is at $x = -1$. We need to find a graph where the turning point (vertex) is at $x = -1$.

To solve this, closely examine the given graphs to identify the one where the parabola's vertex appears at $x = -1$ on the horizontal axis and reflects a symmetry around this axis indicating a minimum point at $y = 0$.

Given the choices in the chart:

• Choice 1 depicts a different vertex or orientation.
• Choice 2 also shows a different shift along the x-axis.
• Choice 3 is correctly showing that the vertex occurs at $x = -1$ with the appropriate configuration indicated by the problem’s prediction.
• Choice 4 does not match the needed features.

Therefore, the graph that matches the equation $y = (x + 1)^2$ is Choice 3, as it is the only graph with the correct vertex point at $(-1, 0)$.

Consequently, the solution to this problem is Choice 3.