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Which of the following is a point on the graph as described by the function y=(2x+1)2−4

?(1 point)
Responses

(1,2)
left parenthesis 1 comma 2 right parenthesis

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis

(−1,−5)

1 answer

To determine which of the given points lies on the graph of the function \( y = (2x + 1)^2 - 4 \), we can evaluate the function for each provided x-coordinate and see if the resulting y-coordinate matches the given y-coordinate of the points.

  1. For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] The point \( (1, 2) \) does not lie on the graph.

  2. For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] The point \( (0, -2) \) does not lie on the graph.

  3. For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] The point \( (-1, -3) \) lies on the graph.

  4. For the point \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] The point \( (-1, -5) \) does not lie on the graph.

Thus, the only point that is on the graph of the function \( y = (2x + 1)^2 - 4 \) is \( \boxed{(-1, -3)} \).