To determine which of the listed points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can evaluate the function for each x-coordinate and check which corresponding y-value matches.
-
For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] So \( (1, 2) \) is not a point on the graph.
-
For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] So \( (-1, -3) \) is a point on the graph.
-
For the point \( (-1, -5) \): Using the previous calculation, we already found \( y = -3 \) when \( x = -1 \). So \( (-1, -5) \) is not on the graph.
-
For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] So \( (0, -2) \) is not a point on the graph.
The only point from the list that lies on the graph of the function is:
\(-1, -3\)