To determine a point on the graph of the function \( y = (2x + 1)^2 - 4 \), you can choose a value for \( x \) and compute \( y \).
Let's evaluate it at \( x = 0 \):
\[ y = (2(0) + 1)^2 - 4 \] \[ y = (1)^2 - 4 \] \[ y = 1 - 4 \] \[ y = -3 \]
So, when \( x = 0 \), \( y = -3 \). This gives us the point \( (0, -3) \).
You can substitute other values for \( x \) to find additional points on the graph as needed. For example, testing \( x = 1 \):
\[ y = (2(1) + 1)^2 - 4 \] \[ y = (3)^2 - 4 \] \[ y = 9 - 4 \] \[ y = 5 \]
This gives us another point: \( (1, 5) \).
So, points on the graph include \( (0, -3) \) and \( (1, 5) \).