To determine which of the given points is on the graph of the function \(y = (2x + 1)^2 - 4\), we can plug in the \(x\)-coordinates of each point into the function and check if the resulting \(y\)-value matches the given \(y\)-coordinate.
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For point (-1, -5): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This yields \((-1, -3)\), so this point is not on the graph.
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For point (-1, -3): We already calculated this for the previous point and found \(y = -3\). Thus, this point is on the graph.
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For point (0, -2): \[ y = (2(0) + 1)^2 - 4 = (1)^2 - 4 = 1 - 4 = -3 \] This yields \((0, -3)\), so this point is not on the graph.
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For point (1, 2): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = (3)^2 - 4 = 9 - 4 = 5 \] This yields \((1, 5)\), so this point is not on the graph.
The only point from the options provided that is on the graph of the function \(y = (2x + 1)^2 - 4\) is (-1, -3).