To determine which of the given points lies on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute the x-coordinate of each point into the function and check if the resulting y-value matches the y-coordinate of the point.
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For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] This does not equal 2.
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For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This matches!
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For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] This does not equal -2.
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For the point \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This does not equal -5.
The only point that lies on the graph is \( (-1, -3) \).