To determine which of the given points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute each \( x \) value from the points into the function and check if the resulting \( y \) value matches.
-
For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (1)^2 - 4 = 1 - 4 = -3 \quad \text{(not -2)} \]
-
For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \quad \text{(matches -3)} \]
-
For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = (3)^2 - 4 = 9 - 4 = 5 \quad \text{(not 2)} \]
-
For the point \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \quad \text{(not -5)} \]
The only point that satisfies the equation is \( (-1, -3) \).
Thus, the correct answer is \( \boxed{(-1, -3)} \).