To determine which points are on the graph of the function \( y = (2x + 1)^2 - 4 \), we can substitute the x-coordinates of each point into the function and see if we get the corresponding y-coordinates.
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For the point \((-1, -5)\): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] The point is \((-1, -3)\), not \((-1, -5)\).
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For the point \((1, 2)\): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] The point is \((1, 5)\), not \((1, 2)\).
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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 point \((-1, -3)\) is on the graph.
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For the point \((0, -2)\): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] The point is \((0, -3)\), not \((0, -2)\).
Thus, the point on the graph is:
\((-1, -3)\).